You never lose that feeling: even after a physics degree, you are exactly Billy for the most advanced topics and so on... You are fundamentally Billy your entire life
as a good friend told me once: "Today we see how stupid we were then and how cool we are now, tomorrow we'll discover how stupid we are how cool we'll be, anyways, we'll always be stupid"
I love these videos. After having studied physics for almost 6 years now, I love remembering these vibes during my fourth and fifth semester. Probably the hardest time of your study (except for the first semester, which obviously only exists to sort out lazy students) when you attended the first quantum mechanics courses just after you were at war with classical mechanics and its weird concepts. It’s that point you felt like nothing makes sense anymore (at least I did).
lmao, 1st semester physics at my uni has Analysis, and not analysis for physicists, we have the mathematician's lecture on it, that's our big filter, and, according to most, the hardest mandatory lecture
@@danielsieker9927 it was for me too, I remember that analysis I is the only written exam I have failed so far, and on almost all of the others I scored the maximum. The written exam was so difficult that still today I reckon it is the toughest exam in the world. I challenge any PhD mathematician to do that monstrosity in two hours aahhaahah.
@@LeonardoRiglietti bro toughest exam in the world? Here in India to get into the best engineering college or IITs students begin to study high level calculus, quantum mechanics and other stuffs from 8th grade. And for every wrong answer there is negative marking. In this exam even 1 marks matters for your score. Students have to study for 9-11 hours a day. I didn't find any exam toughest than JEE (Joint entrance examination). We learn these things in high school. Seems like in high school we are giving answers to university level questions.
@@darkside6610 alright, toughest exam in the world is a hyperbole. We also do university level maths and physics at highschool in Italy if for university level you mean american university level. However, this exam was highly theoretical and very difficult, I would say almost graduate level (surely american graduate level). Still probably the exam you are talking about was harder, I heard lots of terrible stories about it online.
@@darkside6610 in which school teachers teaches calculus in 8th standard.Integration and differentiation is in class 12 syllabus. If you are in any coaching institute they will teach you in class 11. But you are saying you start solving calculus problems in class 8. That's fake
The problem with a lot of these professors is that they live on their own plane of existence, unable to understand why you don't understand. If that makes sense. Had the same problems when studying CS.
Such degrees require loosened screws. I did pure maths and concked out at polar numbers and since then I know hard concepts but simple things are difficult
@@brandonbosire211 quite right, intuition and tunnel vision are big barriers to uni stem. Problem is, young students are taught to manipulate the system before understanding the system itself.
I am a PhD student who hasn't taken physics since hs. I am also mostly a computational scientist, but because my domain sometimes explains matter, I am just now finishing up a QM course this week. My homework grade average is an 87 and my test average is a 60, because without a computer, I am just another Billy🦜. Final exam is next week, lads. Here's hoping I pass. Thank you for posting a window to my soul, Mr. P Solver.
@@juanitome1327 he’s a PhD student with no Physics since highschool. Yet he’s fully capable of passing a quantum mechanics course somehow. I’m also a triple PhD holder taking his first meta theoretical course in master level meta Mathematics and so far I’ve made 0 mistakes in all of my exams and have already had 27 papers published. Wish me luck!
@@blablabla7796 damnn son, I thought I was the only Nobel Prize winner who had disproved Special Relativity and solved the Three Body Problem with black holes' singularities without being able to even read, before the age of 6. Good luck though
@@juanitome1327 it’s great to finally meet people with at least 6 digits of IQ. All of my friends aren’t the brainy types (they’re the sporty types) and they’re preoccupied with sending rockets to mars. I hate it when people waste their brain power on something as mundane as rocket science and quantum mechanics.
As long as you get good at the mathematics BEFORE you use it in physics, it's really easy. If you are a little rusty on the mathematics you are using in a physics class, it becomes so immensely difficult.
When I learned this stuff, the physics lecturers didn't explain to us what was actually mathematically going on. That's the problem. They didn't explain to us what these things meant. What actually mathematically is a ket, or a bra, or an operator, and how do they work? It was only after studying the underlying mathematics of Hilbert spaces and everything on my own that I have developed a better understanding of it all. Here's a trick that will make everything make a lot more sense: Think of kets as infinite dimensional column vectors, bras as infinite dimensional row vectors, and operators as infinite dimensional matrices. Now Dirac notation just becomes linear algebra pretty much :)
Basically, as I understand it, “bra” is a column vector. When you put the two together , that’s a dot product ... a “bra-ket” (geddit?). You can also stick a matrix in-between:
To summarize: High school gives you the equations where all variables are ideal. University gives you the real equations. Since most cases are far from ideal, most of what you learned previously stops existing. Basically, in high school you calculate forces and ignore air resistance, friction, etc. In uni, not only do you calculate those forces, you also take into account the fact that nothing is ever smooth and take into account all the variations. Welcome to quantum physics 😂.
Nope Quantam mechanics is entirely different *not because it have air resistance and real stuff* but is entirely different from mecahnical perspective and cannot he explaned by newtonian mecahnics. Btw, in high school/newtonian mechanics, air resistance is there(in difficult questions, they give expressions of air resistance as a function of velocity and we have to deal accordingly....)
"you speak another language, sir" well, to be fair many quantum physical terms come from German, like eigenvalue, eigenvector (just means "self-value", "self-vector") so he is partially speaking another language.
As a sixth semester student who's just starting on regular QM but researching quantum entanglement, I find it so funny lol it's exactly like that, I'm billy all the way
i love it how complex equations are like one line, with some innocent looking symbols, but if you unravel that shit and actually write down what each of these mean you end up with 2 pages of numbers stacked upon each other in a clusterfuck of matrixes , vectors, operators and other stupid shit and you basically have no idea what's going on anymore. And the professor acts like he's explaining how spoons work, somehow knowing all that ridiculous math off the top of his head.
2:10 The best advice any teacher could give 😮. "Abandon your intuitions. Things don't make sense here." This is legit the easiest way to understand anything 😬. Stop expecting things to make sense. As Richard Feynmann once said: "if you think you understand quantum physics, then you don't understand quantum physics."
@bionx9098 I think it is says that you think that you can predict everything in Quantum Mechanics with nearly 100 precision but in reality you are just hallucinating.
@@bionx9098 it's not really understanding as is, as we live on a scale that is too macroscopic to internalize the "understanding" mentally. however, accepting the innerworkings of QM as they are, usually gives an intuition with which you can predict certain phenomena, after doing quite a bit of math for a month
Evolution of maths : Primary: 1+1=2 Billy : OK.. I get this. High school : (2/6.5)*(5*(4/3)/0.85) Billy : hmm... I can try it. Senior: x+y=z Billy : where the hell the numbers go? Undergrad: *axioms, corollary, calculus* Billy : Is this ancient Spanish? Grad : Numarical analysis, complex analysis, topography.. Billy : Now we r contacting with Aliens? I m not playing it. PhD : 1+1=2 Billy : finally someone understands it.. PhD : not finished it... Prove it... Prepare a thesis book proving it. Billy :😱
@@raja2850 how does that equation even work out? The uncertainty principles tell us that momentum and position of a quantum particle cannot be known at the same time. Hence the speed of an quantum particle needs to uncertain. The definition with the azimuthal orbital number seems to be the more convenient way of defining the angular momentum as it does not rely on Bohr model of atom.
After stripping off consecutive larvae of common sense, adult physicists retain a rudimentary vestige called experience. Therein they differ from the mathematicians
i don't remember all my classes but i remember that the teachers took the time to explain the logic between thing you learn in highschool and university, like the link between the formula
I was preparing for exams 5 minutes ago, raged on operators, threw away the book and decided to enjoy youtube. I have never been gree so much with somebody
As an Asian I deny this, the university part is too easy especially in ASIA you have to pass the test [Phy, Chem & Math's] to get born on the planet Earth and everyone gets 9 months of prep time for the test and then afterwards when we start our first class [kindergarten] with some simple topic ex- Schrödinger equation, Separatrix Separation, Electromagnetism for the Base we have to pass the first [kindergarten Test] with only min 100% passing marks. And you got lots of career options in ASIA like Doctor or Engineer. And idk wtf is TH-camr (Actually I'm not allowed to say this). Thnx >3
1:22 - That is actually the *Reduced* Planck Constant ("h" with a horizontal line towards the top). It is the Planck Constant divided by 2*pi , or h/2π . The Planck Constant is just a normal english "h".
As a high school senior who’s starting to grasp AP Physics 1 topics (momentum, energy, etc.), I’m a bit nervous to see what college will have in store for me as an engineering major with University Physics 😅
@@jarrodangove1921 Some EE use some properties of quantum mechanics but they are not at the level of understanding of physicists and chemists, if your EE course has some quantum it will most likely only apply formulas with almost no theory
1:24 h (the Planck constant) and h-bar (the reduced Planck constant) are two different numbers, you can’t use the name of one and the symbol of the other
As an engine, a vector is a quantity that has both magnitude and direction. Picture it like an arrow: the length represents the magnitude (how much or how big), and the arrowhead points in the direction. Vectors are super handy in physics because they can represent things like force or velocity. Unlike scalars, which are just plain numbers with size, vectors tell us more about movement and change. They can be added together or multiplied by scalars to change their size. When you see them written down, they often have an arrow over the top or are in bold to show they're not just regular numbers. Vectors in the context of complex Hilbert spaces take the concept to a whole new level. In these spaces, vectors are not just arrows in two or three dimensions; they're elements of a complex, infinite-dimensional space. A Hilbert space is a complete space which means it's nicely behaved and all Cauchy sequences converge within the space. The vectors here can represent states in quantum mechanics or functions in a function space. They're subject to operations like addition and scalar multiplication, just like your regular vectors, but also to an inner product, which gives you a way to talk about angles and lengths in this abstract space. This inner product is a generalization of the dot product you might know from 3D vectors, but it works with complex numbers and respects the properties of the space. The cool part about Hilbert spaces is that they allow for the concept of orthogonality and projection, which you can think of as generalizations of perpendicular vectors and shadows in higher dimensions. Vectors in a Hilbert space can be infinitely long lists of numbers or functions, and yet, they still follow similar rules to the simple vectors you'd draw on paper. The beauty of it is that these abstract mathematical concepts are essential in describing the physical world, especially in quantum mechanics. It's a deep and fascinating subject, intertwining algebra, geometry, and the fundamental nature of the universe!
(in my perspective) I swear this is so true and annoying, when I was taking highschool physics all the kids were confident and thought they were smart just for using simple equations like kinematics, Newton's law's, etc. They were too full of themselves. But once they tried the college version of physics. It's a whole different story.
Bra-ket representation for the first time was very scary for me.. Quantum Mechanics from Cohen-Tannoudji is s great book!.. Here in Brazil I also used a book called Mecânica Quântica (author Toledo Piza - a Physics professor from Universidade de São Paulo).
I wouldnt recoment Claude-Cohen (It has 3 volumes) for a beginner, perhaps something a bit more lucid and comprehensive such as "No nonsense introduction to QM". Another book for QM thats my favorite is Theoretical Foundations of Quantum Mechanics by Belal E Baaquie
Do keep in mind, this is all motivated. You SHOULD be taught the regular Schrodinger's Differential Equation, where Hamiltonian is just H = K + U. You get a complex partial differential equation which is pretty daunting. THEN you should be taught how the Hamilton can also be described as a linear operator in Hilbert Space, and how this turns a lot of the math into just linear algebra. And you will see WHY things are complicated, making them more complicated makes the math EASIER to solve!
Most question in JEE advanced are just formed in a way that they look terrifying. But some of them are so tough that even teachers with years of experience will take a day or two to solve 💀
Physics grade 12 in Vietnam: mechanical vibrations, mechanical wave and acoustic wave, AC, quantum physics... General Physics in our university programme just reviews the knowledge in high school physics, but widen and more complicated
If you have a professor like that, I feel for you. But, if you want intuitive explanations, Arthur Beiser's book is where you should be looking. Single handedly carried me through my Quantum Mech course (not doing a physics major).
Should be writing my bachelor thesis right now. Am instead watching the pain of the last three years and hoping i won't have to go back into the quantum realm
@@SimicChameleon Good to know. I am going to be taking Calculus anyways in university (as well as highschool) because I am thinking of studying engineering.
Just gave the final exam again after failing just by 2 marks in different subjects . Its pretty relatable. The physics maths goes above my head on missing just one lecture . Its so stupid that they level up course that much in short amount of time .
Electrical engineering postgrad here :) Did not understand much of the quantum math, but looks funny 🤣 In engineering we have even funnier 3-stage interaction: 1) school. Electricity is easy. Push the lever, current flows in wire, lamp flows. eZyYy. 2) Uni. ELECTRICITY DOES NOT FLOW ON WIRES, BUT ENERGY IS TRANSFERRED IN THE ELECTROMAGNETIC FIELD AROUND THE WIRE. And who cares about all this peasant stuff, here are your 2 years of special math for motor control. Motor only, not generator. Not power lines. 3) Work. Come here you mighty bachelor, we need you to make project documentations, write the whole paperwork, get things bought. Only to be crushed by interaction with actual modern technology, which is literally 40+ years newer then you have been teached. And then you ask in uni, why don't we learn normal modern technology, since we have it in the lab. And you see only bragging like "we have designed schematics in 1981, nothing ever has changed, technology doesn't matter, math über alles.
Tbh they aren't wrong in the sense that technology doesn't matter as long as you understand the math. The math will always be the same, regardless of what tech comes and goes. But, they should have dedicated a module to modern "real worl" tools that you'd use in the world.
@@delq yeah but only for QM. As soon as you do more advanced stuff like QFT you can jump down the cliff with Kratos after seeing the weird ass algebras they are introducing just to ignore it afterwards anyway....
High schooler: centrifugal force isn't real, there's only centripetal force Anyone who knows how to work in non-inertial reference frames: You cannot handle the true power of Spinjitzu
@@eirdonne_ A tensor refers to any numerical or quantitative entity that can undergo changes under a coordinate transformation while preserving its essence. A vector is a particularly illustrative example of a tensor, being a tensor of rank 1. Let us consider a vector in 2D Euclidean space. By rotating the vector around the plane or changing its origin, we can alter its components, but its magnitude or length remains invariant, retaining its meaning. It has been stated that a vector is a tensor of rank one, implying that a single component encodes one dimension of space. On the other hand, a tensor of rank 2 encompasses two-dimensional variables within a single component, enabling us to describe phenomena that involve two dimensions, such as the flux of particles.
Imagine starting with scalars, which are just simple numbers, and then stepping up to vectors, which have magnitude and direction. Tensors go even further; they're multidimensional arrays of numbers that can represent even more complex relationships. Think of them as objects that can take several vectors as input and spit out a scalar or another vector. They're key players in fields like continuum mechanics, where they describe stresses and strains in materials, or in general relativity, where they encapsulate the curvature of spacetime itself! The rank of a tensor tells you how many directions it has. A rank-0 tensor is just a scalar, rank-1 is a vector, and from there, it just explodes into an n-dimensional frenzy. Tensors obey certain transformation rules that keep their essential nature the same, even when you change how you describe your system-like changing from imperial to metric or shifting your viewpoint in space. Tensors are mathematical beasts that help us describe and navigate the complexities of the universe, from the way objects move and interact, to the very fabric of reality itself. They're not just numbers on a page; they're the backbone of our understanding of everything from engineering to cosmology. In general relativity, tensors are the stars of the show. The most famous tensor here is the Einstein field equations' star player, the Einstein tensor. This tensor encapsulates the curvature of spacetime caused by mass and energy. What it's saying is that the geometry of spacetime tells matter how to move, and the distribution of matter tells spacetime how to curve. It's like a cosmic dance, with the curvature and matter leading and following each other. The metric tensor is another VIP in general relativity. It describes the distance between points in spacetime, which is super weird because it's not just space-it's space and time mixed together. This tensor lets us calculate how time dilates and lengths contract when you're zooming near the speed of light or chilling near a massive object like a black hole. To solve the Einstein field equations, you need to juggle these tensors and work out how the metric tensor evolves in the presence of matter and energy. The solutions to these equations are what predict the existence of black holes, the expansion of the universe, and even gravitational waves-ripples in the fabric of spacetime itself! So, tensors in general relativity are like the language the universe uses to describe its own shape and evolution. It's a challenging language, for sure, but it's also incredibly beautiful and profound.
In high school, you learn classical physics. This is sufficient for most everyday things that are roughly human scale. Classical physics is a good enough approximation for most things, but is not the full reality. As soon as you start dealing with things that are very small (the scale of molecules), very large (the scale of planets), or speeds that approach the speed of light, classical physics breaks down, and you need to use quantum mechanics, general and special relativity respectively.
Remember though your professors don’t know everything! You could easily solve a new and useful thing. Quantum momentum is the eventual result of unsimple position and velocity, and explains macro momentum. 1:42 Fun video!
Just lived through a monster "Physics 2" course that went heavy into quantum also.... hilariously I recognize some of the formulas in this sketch; but I'm still billy, ultimately.
Ek = 1/2 mv^2 = p^2/2m The Ek operator is defined as p^2/2m, where p = -ih/2π d/dx Ek = (-ih/2π)^2 d^2/dx^2 / 2m = -h^2/8mπ^2 d^2/dx^2 hope this helps :)
Fun fact, i did laaaaattteee studies (stopped school early then get back after my french majority) and entered universities at 25 (by taking quick lessons called DAEU in france as shortcut) i had no idea what vector was my professor was trying to explain me ( pre universitary normal cursus lessons) so i tried my best to understand what it was Our first physic exam was 90% around that, i did 2 double page of paper exam. I was pretty happy but not confident to have more than 12/20 (in france our notation is based on point sor 10/20 is median, 20/20 is perfect) Two weeks later the result were put on the big university board. 0/20 ..... I never went again in physics class 😂
As a Biochemistry student, I would say I'm glad I don't have to know all this... But we aren't safe either, Physical Chemistry II is just a disguise for Quantum Mechanics. The bits of the video where things just straight up don't have position or momentum anymore was fucking hilarious.
Actually there is a precise definition of momentum that covers all of momentum you need to know. Momentum is a quantity that is connected to space translation invariance in the sense of Noethers theorem.
High school physics was a joke compared to university level physics. My High School Physics class required knowledge of algebra, geometry and trigonometry and it was a piece of cake. My lower division physics class required knowledge of these branches of mathematics plus Calculus 1 and 2 and a background in High Physics is recommended but not required. I would say it was medium (it was neither hard nor easy). Upper division Physics classes require knowledge of these math classes plus Linear Algebra, Calculus 3/Multi-variable/Vector Calculus and Differential Equations and knowledge of lower division Physics. If you struggled with any of these classes, you are fucked in upper division Physics classes. And if you think upper division Physics was tough, Graduate division Physics is Armageddon. High School Physics = easy Lower Division Physics/AP Physics = medium Upper Division Physics = hard Graduate Division Physics = Armageddon/hell
Complex numbers are integral to the Schrödinger equation, which is the fundamental equation of motion in non-relativistic quantum mechanics. The equation itself is a partial differential equation that describes how the quantum state of a physical system changes over time. Complex numbers come into play because the wave function, which contains all the information about the system's state, is a complex-valued function. The use of complex numbers allows the wave function to encode not just the probability distribution of the particle's position (which is given by the square of the absolute value of the wave function) but also the phase information, which is crucial for understanding interference and diffraction patterns that are characteristic of quantum systems. The imaginary unit, denoted as 'i', is what enables the wave function to oscillate without bounds in amplitude, which would be impossible with only real numbers. Furthermore, the Schrödinger equation involves the Laplacian operator, which when applied to the wave function, requires the complex conjugate to calculate observables, such as energy or momentum. The complex exponential, e^(iθ), where θ is a real number, is a key component in describing these oscillations and is essential for representing the time evolution of the wave function. This representation is rooted in Euler's formula, which connects complex exponentials with trigonometric functions, allowing for a comprehensive description of the quantum behavior of particles.
@@rubikscubechannel6588 bro hahaha you didn't really make it much easier with this kind of an explanation lmao, but you're completely right most important part: complex numbers allow to encode phase differences of wavefunctions, which makes interferention much easier to calculate however, you can define QM in terms of sines and cosines, without complex numbers (!), but the expressions to write it down that way look horrific
You never lose that feeling: even after a physics degree, you are exactly Billy for the most advanced topics and so on... You are fundamentally Billy your entire life
as a good friend told me once:
"Today we see how stupid we were then and how cool we are now, tomorrow we'll discover how stupid we are how cool we'll be, anyways, we'll always be stupid"
It’s called the billy constant
True
How do I escape from being Billy forever?
@@unrivaledunderthesun become god, or die
I love these videos. After having studied physics for almost 6 years now, I love remembering these vibes during my fourth and fifth semester. Probably the hardest time of your study (except for the first semester, which obviously only exists to sort out lazy students) when you attended the first quantum mechanics courses just after you were at war with classical mechanics and its weird concepts. It’s that point you felt like nothing makes sense anymore (at least I did).
lmao, 1st semester physics at my uni has Analysis, and not analysis for physicists, we have the mathematician's lecture on it, that's our big filter, and, according to most, the hardest mandatory lecture
@@danielsieker9927 it was for me too, I remember that analysis I is the only written exam I have failed so far, and on almost all of the others I scored the maximum. The written exam was so difficult that still today I reckon it is the toughest exam in the world. I challenge any PhD mathematician to do that monstrosity in two hours aahhaahah.
@@LeonardoRiglietti bro toughest exam in the world? Here in India to get into the best engineering college or IITs students begin to study high level calculus, quantum mechanics and other stuffs from 8th grade. And for every wrong answer there is negative marking. In this exam even 1 marks matters for your score. Students have to study for 9-11 hours a day. I didn't find any exam toughest than JEE (Joint entrance examination). We learn these things in high school. Seems like in high school we are giving answers to university level questions.
@@darkside6610 alright, toughest exam in the world is a hyperbole. We also do university level maths and physics at highschool in Italy if for university level you mean american university level. However, this exam was highly theoretical and very difficult, I would say almost graduate level (surely american graduate level). Still probably the exam you are talking about was harder, I heard lots of terrible stories about it online.
@@darkside6610 in which school teachers teaches calculus
in 8th standard.Integration and differentiation is in class 12 syllabus. If you are in any coaching institute they will teach you in class 11. But you are saying you start solving calculus problems in class 8. That's fake
Now I know why Billy has changed for software engineering afterwards. 😂
Are you suggesting that it's easier?
Update: I'm a freshman in electrical engineering and yeah physics is harder, A LOT harder...
@@darkdelphin834 no suggestion, it is easier
@@mayukhchakraborty5364 can confirm
As a software developer that took an intro to physics course in college, I can 100% confirm development is easier than physics.
U can literally create a universe inside a pc withought needing all that quantum physics crap!
As a physics student whose courses are slowly transforming into these I can say I want my secondary school physics back
As a physics student who is a junior in college, I concur.
The problem with a lot of these professors is that they live on their own plane of existence, unable to understand why you don't understand. If that makes sense.
Had the same problems when studying CS.
Such degrees require loosened screws. I did pure maths and concked out at polar numbers and since then I know hard concepts but simple things are difficult
@@brandonbosire211 quite right, intuition and tunnel vision are big barriers to uni stem. Problem is, young students are taught to manipulate the system before understanding the system itself.
To be honest. When bro said that they're unable to understand why you don't understand, memories came flooding in
"Unable to understand why we don't understand" isn't that like all the teachers?!
@@brandonbosire211 wtf are polar numbers💀
I am a PhD student who hasn't taken physics since hs. I am also mostly a computational scientist, but because my domain sometimes explains matter, I am just now finishing up a QM course this week.
My homework grade average is an 87 and my test average is a 60, because without a computer, I am just another Billy🦜.
Final exam is next week, lads. Here's hoping I pass. Thank you for posting a window to my soul, Mr. P Solver.
What is the point of this comment
@@juanitome1327 he’s a PhD student with no Physics since highschool. Yet he’s fully capable of passing a quantum mechanics course somehow. I’m also a triple PhD holder taking his first meta theoretical course in master level meta Mathematics and so far I’ve made 0 mistakes in all of my exams and have already had 27 papers published. Wish me luck!
@@blablabla7796 damnn son, I thought I was the only Nobel Prize winner who had disproved Special Relativity and solved the Three Body Problem with black holes' singularities without being able to even read, before the age of 6. Good luck though
@@juanitome1327 it’s great to finally meet people with at least 6 digits of IQ. All of my friends aren’t the brainy types (they’re the sporty types) and they’re preoccupied with sending rockets to mars. I hate it when people waste their brain power on something as mundane as rocket science and quantum mechanics.
Best of luck!
As long as you get good at the mathematics BEFORE you use it in physics, it's really easy. If you are a little rusty on the mathematics you are using in a physics class, it becomes so immensely difficult.
I agree 💯
it becomes easy to calculate, yes, but not much easier to understand hahaha
When I learned this stuff, the physics lecturers didn't explain to us what was actually mathematically going on. That's the problem. They didn't explain to us what these things meant. What actually mathematically is a ket, or a bra, or an operator, and how do they work? It was only after studying the underlying mathematics of Hilbert spaces and everything on my own that I have developed a better understanding of it all.
Here's a trick that will make everything make a lot more sense: Think of kets as infinite dimensional column vectors, bras as infinite dimensional row vectors, and operators as infinite dimensional matrices. Now Dirac notation just becomes linear algebra pretty much :)
Huh
You speak the prof language
Went over my head, pls translate
This really helps! Thank you for your insight and wisdom.
Basically, as I understand it, “bra” is a column vector. When you put the two together , that’s a dot product ... a “bra-ket” (geddit?). You can also stick a matrix in-between:
To summarize:
High school gives you the equations where all variables are ideal.
University gives you the real equations. Since most cases are far from ideal, most of what you learned previously stops existing.
Basically, in high school you calculate forces and ignore air resistance, friction, etc. In uni, not only do you calculate those forces, you also take into account the fact that nothing is ever smooth and take into account all the variations. Welcome to quantum physics 😂.
Nope
Quantam mechanics is entirely different *not because it have air resistance and real stuff* but is entirely different from mecahnical perspective and cannot he explaned by newtonian mecahnics.
Btw, in high school/newtonian mechanics, air resistance is there(in difficult questions, they give expressions of air resistance as a function of velocity and we have to deal accordingly....)
no, thankyou. i’m leaving. not my major
Well in india we do consider air resistance, friction, mass of string etc.. in standard 11
Air resistance and friction were included to physics in my country back in high school.
Mm... As someone from grade 11th struggling of physics... What should i even say....
"you speak another language, sir" well, to be fair many quantum physical terms come from German, like eigenvalue, eigenvector (just means "self-value", "self-vector") so he is partially speaking another language.
As a sixth semester student who's just starting on regular QM but researching quantum entanglement, I find it so funny lol it's exactly like that, I'm billy all the way
regular QM ? There are different QM now ?
@@dudono1744 There's normal QM, and then relativistic QM, the latter of these is realised through Quantum Field Theory
kind of specific for quantum mechanics, but overall spot on. Best vid in this series
i love it how complex equations are like one line, with some innocent looking symbols, but if you unravel that shit and actually write down what each of these mean you end up with 2 pages of numbers stacked upon each other in a clusterfuck of matrixes , vectors, operators and other stupid shit and you basically have no idea what's going on anymore.
And the professor acts like he's explaining how spoons work, somehow knowing all that ridiculous math off the top of his head.
matrices*
Dude I am doing PhD in physics like yourself. This is funniest thing I have seen all week. Btw I also showed you math video to my students.
2:10 The best advice any teacher could give 😮. "Abandon your intuitions. Things don't make sense here." This is legit the easiest way to understand anything 😬. Stop expecting things to make sense. As Richard Feynmann once said: "if you think you understand quantum physics, then you don't understand quantum physics."
But that doesn’t make sense. How can understand something by not understanding
@@bionx9098 “Things don't make sense anymore”
@bionx9098 I think it is says that you think that you can predict everything in Quantum Mechanics with nearly 100 precision but in reality you are just hallucinating.
@@bionx9098 it's not really understanding as is, as we live on a scale that is too macroscopic to internalize the "understanding" mentally. however, accepting the innerworkings of QM as they are, usually gives an intuition with which you can predict certain phenomena, after doing quite a bit of math for a month
Evolution of maths :
Primary: 1+1=2
Billy : OK.. I get this.
High school : (2/6.5)*(5*(4/3)/0.85)
Billy : hmm... I can try it.
Senior: x+y=z
Billy : where the hell the numbers go?
Undergrad: *axioms, corollary, calculus*
Billy : Is this ancient Spanish?
Grad : Numarical analysis, complex analysis, topography..
Billy : Now we r contacting with Aliens? I m not playing it.
PhD : 1+1=2
Billy : finally someone understands it..
PhD : not finished it... Prove it... Prepare a thesis book proving it.
Billy :😱
Topology, topography is not math I think
@@zhangkevin6748 algebraic topology is part of mathematics.
@@EldhoseJoseph No, OP typed topography instead of topology.
Blud really said topography
Also 1+1=2 is a very elementary proof in abstract algebra final level should be Riemann hypothesis stuff like that lmao
2:11 "Abandon your intuitions
things dont make sense here."
Nice when the professor says something we all can understand.
That was only linear momentum. There's also angular momentum.
Oh QM has angular momentum too! Infact, its even quantized and has no classical intuition as to why it is the way it is :) have fun
@@trollnat9857 MVR=nh/2π . Studied that in atomic structure. And that too in eleventh.
@@raja2850 probably u are indian ..as I have studied in that chapter too
@@adityabaroniya9343 yes
@@raja2850 how does that equation even work out? The uncertainty principles tell us that momentum and position of a quantum particle cannot be known at the same time. Hence the speed of an quantum particle needs to uncertain. The definition with the azimuthal orbital number seems to be the more convenient way of defining the angular momentum as it does not rely on Bohr model of atom.
These videos are actually pretty good especially the programming ones. Its not just mindless but you actually learn something by the end.
It’s crazy how it’s PRETTY MUCH the same but throw in different letters and symbols and we all have mental breakdowns 😂
Fantastic this meme perfectly captures the Dunning-Kruger curve that all physics students experience :) but we'll all get there in the end ! ... maybe
After stripping off consecutive larvae of common sense, adult physicists retain a rudimentary vestige called experience. Therein they differ from the mathematicians
i don't remember all my classes but i remember that the teachers took the time to explain the logic between thing you learn in highschool and university, like the link between the formula
I hope I get a teacher that explanes the logic too
@@admiraloscar3320 give up just hoping, try asking questions to professors
I was preparing for exams 5 minutes ago, raged on operators, threw away the book and decided to enjoy youtube. I have never been gree so much with somebody
As an Asian I deny this, the university part is too easy especially in ASIA you have to pass the test [Phy, Chem & Math's] to get born on the planet Earth and everyone gets 9 months of prep time for the test and then afterwards when we start our first class [kindergarten] with some simple topic ex- Schrödinger equation, Separatrix Separation, Electromagnetism for the Base we have to pass the first [kindergarten Test] with only min 100% passing marks. And you got lots of career options in ASIA like Doctor or Engineer.
And idk wtf is TH-camr (Actually I'm not allowed to say this).
Thnx >3
🤣🤣
Are you talking about JEE? Korean SAT? Or GAOKAO?
You forgot the supersymmetric string theory .
r/iamverysmart
@@ericzhan3454 think it’s a joke bro
Professor went from classical mode to quantum mode real quick 😂😂
1:36 Ah I get it… ASGORE is playing because the Professor is basically killing Billy’s childlike determination to learn physics!
literally one of the most difficult, most advanced, hardest class ever in history. not even other classes can be superior to physics.
Last two semesters of physics degree I felt like Billy
1:22 - That is actually the *Reduced* Planck Constant ("h" with a horizontal line towards the top). It is the Planck Constant divided by 2*pi , or h/2π . The Planck Constant is just a normal english "h".
Physicists are too lazy to say "reduced planck constant", you'll be lucky if they even say "h-bar" or if you can read their hieroglyphics.
Thanks
As a high school senior who’s starting to grasp AP Physics 1 topics (momentum, energy, etc.), I’m a bit nervous to see what college will have in store for me as an engineering major with University Physics 😅
Ya really don’t touch quantum mechanics in engineering unless you’re trying to self harm. Or you’re doing EE. Same thing I guess
@@jarrodangove1921 Some EE use some properties of quantum mechanics but they are not at the level of understanding of physicists and chemists, if your EE course has some quantum it will most likely only apply formulas with almost no theory
im gonna engineering major next year too. I'm studying for my exams in two weeks wish me luck mate
@@ultraclipz3230Hope you’re doing well man!! 2nd semester of Civil Engineering just started for me at RPI, we’re cooking. Hbu?
1:24 h (the Planck constant) and h-bar (the reduced Planck constant) are two different numbers, you can’t use the name of one and the symbol of the other
Used to have (y=mx + c ) and now generalised least squares model in a matrix form which needs optimisation in order to solve the parameters. 😭
As a mathatics guy, a vector is an element of a vector space
mathematics*
As an engine, a vector is a quantity that has both magnitude and direction. Picture it like an arrow: the length represents the magnitude (how much or how big), and the arrowhead points in the direction. Vectors are super handy in physics because they can represent things like force or velocity. Unlike scalars, which are just plain numbers with size, vectors tell us more about movement and change. They can be added together or multiplied by scalars to change their size. When you see them written down, they often have an arrow over the top or are in bold to show they're not just regular numbers. Vectors in the context of complex Hilbert spaces take the concept to a whole new level. In these spaces, vectors are not just arrows in two or three dimensions; they're elements of a complex, infinite-dimensional space. A Hilbert space is a complete space which means it's nicely behaved and all Cauchy sequences converge within the space.
The vectors here can represent states in quantum mechanics or functions in a function space. They're subject to operations like addition and scalar multiplication, just like your regular vectors, but also to an inner product, which gives you a way to talk about angles and lengths in this abstract space. This inner product is a generalization of the dot product you might know from 3D vectors, but it works with complex numbers and respects the properties of the space. The cool part about Hilbert spaces is that they allow for the concept of orthogonality and projection, which you can think of as generalizations of perpendicular vectors and shadows in higher dimensions. Vectors in a Hilbert space can be infinitely long lists of numbers or functions, and yet, they still follow similar rules to the simple vectors you'd draw on paper. The beauty of it is that these abstract mathematical concepts are essential in describing the physical world, especially in quantum mechanics. It's a deep and fascinating subject, intertwining algebra, geometry, and the fundamental nature of the universe!
Highschool mechanics and then at university: technical acoustics
i lost my eigenvalue watching this
video really applies that annihilation operator to the ground state of my mental well-being
I like how the beeps get angrier when Billy gets upset
(in my perspective) I swear this is so true and annoying, when I was taking highschool physics all the kids were confident and thought they were smart just for using simple equations like kinematics, Newton's law's, etc. They were too full of themselves. But once they tried the college version of physics. It's a whole different story.
Im a grad student and I still feel like Billy whenever a new concept pops up
I’m taking AP physics 1 right now and you’re scaring me as to what I’ll find in C next year
It calculus version physics. 1 is newton mechanic and 2 is electricity magnetism class
Bra-ket representation for the first time was very scary for me.. Quantum Mechanics from Cohen-Tannoudji is s great book!.. Here in Brazil I also used a book called Mecânica Quântica (author Toledo Piza - a Physics professor from Universidade de São Paulo).
I wouldnt recoment Claude-Cohen (It has 3 volumes) for a beginner, perhaps something a bit more lucid and comprehensive such as "No nonsense introduction to QM". Another book for QM thats my favorite is Theoretical Foundations of Quantum Mechanics by Belal E Baaquie
Do keep in mind, this is all motivated. You SHOULD be taught the regular Schrodinger's Differential Equation, where Hamiltonian is just H = K + U. You get a complex partial differential equation which is pretty daunting. THEN you should be taught how the Hamilton can also be described as a linear operator in Hilbert Space, and how this turns a lot of the math into just linear algebra. And you will see WHY things are complicated, making them more complicated makes the math EASIER to solve!
0:18 "There's nowhere to run!"
This is the line that comes in my head when i hear that music
When you realise even the simple grade 12 physics has its own share of terrifying questions.
Just watch the JEE advanced question paper.
Bruh there r puzzle books with harder problems with no prerequisites...what point r u tryna make
Most question in JEE advanced are just formed in a way that they look terrifying. But some of them are so tough that even teachers with years of experience will take a day or two to solve 💀
I shared it to my nuclear physicist dad after we had laughed so much
I just had quantum exam, I could't breath during the exam.
Physics grade 12 in Vietnam: mechanical vibrations, mechanical wave and acoustic wave, AC, quantum physics... General Physics in our university programme just reviews the knowledge in high school physics, but widen and more complicated
1:22 isnt plancks constant just a normal 'h'
if I remember correctly that notation is "h cross" or h/(2pi)
its for a monoelectronic atomic species only
If you have a professor like that, I feel for you. But, if you want intuitive explanations, Arthur Beiser's book is where you should be looking. Single handedly carried me through my Quantum Mech course (not doing a physics major).
Bro used h cross instead of h as Planck's constant ☠
h cross is (h/2 pie) lol
1.055 x 10-³⁴ J s-¹
Should be writing my bachelor thesis right now. Am instead watching the pain of the last three years and hoping i won't have to go back into the quantum realm
Bro said h cross as planck constant😂
"You speak another language sir. I quit"
Billy graduated with a degree in art
As a highschool student currently taking Grade 11 Physics, this video has saved me from making the mistake of studying physics in university.
do it
It just requires calculus series to study university physics.
@@SimicChameleon Good to know. I am going to be taking Calculus anyways in university (as well as highschool) because I am thinking of studying engineering.
@@Mr.LeoWarren Fool.
@@Lembdadelta Why?
Just gave the final exam again after failing just by 2 marks in different subjects . Its pretty relatable. The physics maths goes above my head on missing just one lecture . Its so stupid that they level up course that much in short amount of time .
I'm convinced all professors spout meaningless bollocks because nobody actually understands the topic enough to contradict them.
Fun fact: 1:21 represents a cyrillic letter (Soft C), It's used in my language lol its looks like a h but with a line
As I am currently halfway through AP physics , this is accurate
Electrical engineering postgrad here :)
Did not understand much of the quantum math, but looks funny 🤣
In engineering we have even funnier 3-stage interaction:
1) school. Electricity is easy. Push the lever, current flows in wire, lamp flows. eZyYy.
2) Uni. ELECTRICITY DOES NOT FLOW ON WIRES, BUT ENERGY IS TRANSFERRED IN THE ELECTROMAGNETIC FIELD AROUND THE WIRE. And who cares about all this peasant stuff, here are your 2 years of special math for motor control. Motor only, not generator. Not power lines.
3) Work. Come here you mighty bachelor, we need you to make project documentations, write the whole paperwork, get things bought. Only to be crushed by interaction with actual modern technology, which is literally 40+ years newer then you have been teached.
And then you ask in uni, why don't we learn normal modern technology, since we have it in the lab. And you see only bragging like "we have designed schematics in 1981, nothing ever has changed, technology doesn't matter, math über alles.
Tbh they aren't wrong in the sense that technology doesn't matter as long as you understand the math. The math will always be the same, regardless of what tech comes and goes. But, they should have dedicated a module to modern "real worl" tools that you'd use in the world.
Tbh the math for QM is much simpler
@@delq yeah but only for QM. As soon as you do more advanced stuff like QFT you can jump down the cliff with Kratos after seeing the weird ass algebras they are introducing just to ignore it afterwards anyway....
@@FakeNewsMonthly i agree, it went downhill from relativistic electrodynamics onwards atleast for me
We all know the real reason the tech is outdated, professors are old and don't want to put in the effort to get up-to-date.
that's literally me when I am in the first class of quantum chemistry introductory course
bruhh i actually learned from this no cap fr fr
1:22 is reduced plancks constant. plancks constant divided by 2pi
"sir you speak another language, i quit" was hilarious as hell
I just want to say that I recommend the t-shirt, I get +10 to my Python skillz with it :)
Bro used a hash and called it plancks constant😭
Where is my newtonian mecanic with neglected friction ? Please give it back.
Thank you so much for making these videos. ;_;
0:41 billy space travel
High schooler: centrifugal force isn't real, there's only centripetal force
Anyone who knows how to work in non-inertial reference frames: You cannot handle the true power of Spinjitzu
Ninjagoooooo
university physics: gravity is not a real force either
Conclusion :
Middle school: Things exist in 3d
High school: Thing exist in 4d
"What's a tensor?"
"Oh, a tensor is just something that transforms like a tensor"
"so... whats a tensor?"
@@eirdonne_ A tensor refers to any numerical or quantitative entity that can undergo changes under a coordinate transformation while preserving its essence. A vector is a particularly illustrative example of a tensor, being a tensor of rank 1. Let us consider a vector in 2D Euclidean space. By rotating the vector around the plane or changing its origin, we can alter its components, but its magnitude or length remains invariant, retaining its meaning. It has been stated that a vector is a tensor of rank one, implying that a single component encodes one dimension of space. On the other hand, a tensor of rank 2 encompasses two-dimensional variables within a single component, enabling us to describe phenomena that involve two dimensions, such as the flux of particles.
Imagine starting with scalars, which are just simple numbers, and then stepping up to vectors, which have magnitude and direction. Tensors go even further; they're multidimensional arrays of numbers that can represent even more complex relationships. Think of them as objects that can take several vectors as input and spit out a scalar or another vector. They're key players in fields like continuum mechanics, where they describe stresses and strains in materials, or in general relativity, where they encapsulate the curvature of spacetime itself! The rank of a tensor tells you how many directions it has. A rank-0 tensor is just a scalar, rank-1 is a vector, and from there, it just explodes into an n-dimensional frenzy. Tensors obey certain transformation rules that keep their essential nature the same, even when you change how you describe your system-like changing from imperial to metric or shifting your viewpoint in space. Tensors are mathematical beasts that help us describe and navigate the complexities of the universe, from the way objects move and interact, to the very fabric of reality itself. They're not just numbers on a page; they're the backbone of our understanding of everything from engineering to cosmology.
In general relativity, tensors are the stars of the show. The most famous tensor here is the Einstein field equations' star player, the Einstein tensor. This tensor encapsulates the curvature of spacetime caused by mass and energy. What it's saying is that the geometry of spacetime tells matter how to move, and the distribution of matter tells spacetime how to curve. It's like a cosmic dance, with the curvature and matter leading and following each other. The metric tensor is another VIP in general relativity. It describes the distance between points in spacetime, which is super weird because it's not just space-it's space and time mixed together. This tensor lets us calculate how time dilates and lengths contract when you're zooming near the speed of light or chilling near a massive object like a black hole. To solve the Einstein field equations, you need to juggle these tensors and work out how the metric tensor evolves in the presence of matter and energy. The solutions to these equations are what predict the existence of black holes, the expansion of the universe, and even gravitational waves-ripples in the fabric of spacetime itself! So, tensors in general relativity are like the language the universe uses to describe its own shape and evolution. It's a challenging language, for sure, but it's also incredibly beautiful and profound.
@@rubikscubechannel6588 this is actually very helpful, thank you!
The title should be classical phy vs quantum phy😂😂
When you start using one of the most forgiven but also coolest letters in existence (Ψ, ψ; the psi) in math, you know that you’re f*cked up
Lmfao it is my duty as professor that you don't even try to understand them
You make the content I want to see. Thank you 🙏🏻
I was thinking of pursuing physics for graduation in college, thx I'll stick to my plans on doing Bachelor of Technology instead
The background music choice is impeccable
Billy went to rank 3000th university in the world.
I wish billy was my friend irl lol. Would've been a blast
When billy said :- naah bro where's my momentum p=mv it looked really innocent
In high school, you learn classical physics. This is sufficient for most everyday things that are roughly human scale. Classical physics is a good enough approximation for most things, but is not the full reality. As soon as you start dealing with things that are very small (the scale of molecules), very large (the scale of planets), or speeds that approach the speed of light, classical physics breaks down, and you need to use quantum mechanics, general and special relativity respectively.
Remember though your professors don’t know everything! You could easily solve a new and useful thing. Quantum momentum is the eventual result of unsimple position and velocity, and explains macro momentum. 1:42 Fun video!
Just lived through a monster "Physics 2" course that went heavy into quantum also.... hilariously I recognize some of the formulas in this sketch; but I'm still billy, ultimately.
Ek = 1/2 mv^2 = p^2/2m
The Ek operator is defined as p^2/2m, where p = -ih/2π d/dx
Ek = (-ih/2π)^2 d^2/dx^2 / 2m = -h^2/8mπ^2 d^2/dx^2
hope this helps :)
Fun fact, i did laaaaattteee studies (stopped school early then get back after my french majority) and entered universities at 25 (by taking quick lessons called DAEU in france as shortcut) i had no idea what vector was my professor was trying to explain me ( pre universitary normal cursus lessons) so i tried my best to understand what it was
Our first physic exam was 90% around that, i did 2 double page of paper exam. I was pretty happy but not confident to have more than 12/20 (in france our notation is based on point sor 10/20 is median, 20/20 is perfect)
Two weeks later the result were put on the big university board.
0/20 .....
I never went again in physics class 😂
Just look at the hamiltonian, its literally the same as kinetic plus Potential energy, so ez
'Just diagonalize the Hamiltonian' is a perfect summary of my life during undergrad physics lol
As a Biochemistry student, I would say I'm glad I don't have to know all this...
But we aren't safe either, Physical Chemistry II is just a disguise for Quantum Mechanics. The bits of the video where things just straight up don't have position or momentum anymore was fucking hilarious.
Actually there is a precise definition of momentum that covers all of momentum you need to know. Momentum is a quantity that is connected to space translation invariance in the sense of Noethers theorem.
no wonder why my parents suggest me to do college physics as my first time studying physics. I am screwed
Much mv²/2, very cool 👍
Would be amazing to see all the basic physics condensed into a 3 minute video 🙃
Me just beginning my grade 10 with physics as my favourite subject.....💀💀💀💀
Physics will show u 50 shades of grey in 3D❤😂😂😂😂😂
HAHAHAHAHAHAHAH
I expected to see a joke about vector, pseudovector and maybe spinor
That time when you are introduced to Lagrange and Hamilton and then came QM....
1:31 pain background music
Naruto fans why didn't you notice?
High school physics was a joke compared to university level physics. My High School Physics class required knowledge of algebra, geometry and trigonometry and it was a piece of cake. My lower division physics class required knowledge of these branches of mathematics plus Calculus 1 and 2 and a background in High Physics is recommended but not required. I would say it was medium (it was neither hard nor easy). Upper division Physics classes require knowledge of these math classes plus Linear Algebra, Calculus 3/Multi-variable/Vector Calculus and Differential Equations and knowledge of lower division Physics. If you struggled with any of these classes, you are fucked in upper division Physics classes. And if you think upper division Physics was tough, Graduate division Physics is Armageddon.
High School Physics = easy
Lower Division Physics/AP Physics = medium
Upper Division Physics = hard
Graduate Division Physics = Armageddon/hell
and in my country we study that university physics in grade 11 and 12
Nah , how about explaining the use of complex numbers in Schrodinger equation , that will do it
Complex numbers are integral to the Schrödinger equation, which is the fundamental equation of motion in non-relativistic quantum mechanics. The equation itself is a partial differential equation that describes how the quantum state of a physical system changes over time. Complex numbers come into play because the wave function, which contains all the information about the system's state, is a complex-valued function. The use of complex numbers allows the wave function to encode not just the probability distribution of the particle's position (which is given by the square of the absolute value of the wave function) but also the phase information, which is crucial for understanding interference and diffraction patterns that are characteristic of quantum systems. The imaginary unit, denoted as 'i', is what enables the wave function to oscillate without bounds in amplitude, which would be impossible with only real numbers.
Furthermore, the Schrödinger equation involves the Laplacian operator, which when applied to the wave function, requires the complex conjugate to calculate observables, such as energy or momentum. The complex exponential, e^(iθ), where θ is a real number, is a key component in describing these oscillations and is essential for representing the time evolution of the wave function. This representation is rooted in Euler's formula, which connects complex exponentials with trigonometric functions, allowing for a comprehensive description of the quantum behavior of particles.
@@rubikscubechannel6588 bro hahaha you didn't really make it much easier with this kind of an explanation lmao, but you're completely right
most important part: complex numbers allow to encode phase differences of wavefunctions, which makes interferention much easier to calculate
however, you can define QM in terms of sines and cosines, without complex numbers (!), but the expressions to write it down that way look horrific
On a heavier subject, talking about fields in quantum and classical mechanics is a whole different thing
Habibi Come to India, USA University QUESTIONS = Indian ADV JEE QUESTIONS 😂😂🤣🤣
Example? Tensor integration, Schrodinger eqn, Hamiltonian, Lagrange, comp. Analysis.....more
@@BOT........ Yea lol they are in Jee advanced exam, should be written at age of 17.
@@allenmano can you send me any questions of jee or link
@@BOT........ I remember Tibess trying one of the hard question in IIT physics,
th-cam.com/video/TxXuo9ukVxU/w-d-xo.htmlfeature=shared
@@BOT........ Normal questions expected to solve around 3 mins hard ones are 5 if you are expecting a desent rank for a branch.