Excellent episode! Masterful explanation of a very difficult topic. Couldn't have done it better myself. I won't need to make a video on this topic, as I will just refer people to yours. Ha.
You're brilliant. Clearest explanation of this I've seen. I love how you didn't really assume any prior knowledge and explained every step; this was just what I needed.
this was more than a clear explanation, he took the arrogant-physics-genius-higher-intelligence-explanation ingredient that's baked into learning physics, out
Phys Major here, really glad you posted this. just shows whats up ahead for me in junior year. The walk-through was good, really. Makes one excited for their 1st QM course.
Wish we had a resource like this back in my day. We were chucked in straight at the deep end with heavy-duty bra-ket notation, operators and the rest of it. Needless to say, I never got a good qualitative understanding and grounding in of QM, and essentially had to blag my way through the remainder of my course.
You Sir are extremely talented. This is probably the clearest, most elegant description of solving the wave equation I have ever seen uploaded to TH-cam. Congratulations!
Studied Chemistry in the second half of the 80´s. Phyiscs and this topic was also part of it. We solved it for Hydrogen. It was really fun (no sarcasm). But still today (around + 35 years later) I could´nt get my head around the fact that time has to be eleminated / ignored in the first step. Seems to me that time does does not exists. Waiting for someone who figures out that the dimensions are curled one quantum level and that this is the reason why we experience time, the (non-force) effect of gravity, black matter and energy and strange things, like time bending, when "we go closer" to (massive) objects / black holes ... Pretty sure some one will find out that black holes are not singularities. Black holes are the oposite. Starting with the event of horiziont the dimension are so far "un-curled" (= straight) that (from our point of view) we could not "see" beyond our > 3 dimensions because at this point there are way more dimensions. So black holes aren´t holes they are the opposite, they are columns. lol . greek mythology came in my mind ... Didnt they say that the world is carried by Atlas and columns?
I’m in modern physics 2 and we deal with the Schrödinger equation all the time. This is the best and most concise explanation of the Schrödinger equation, boundary conditions, particle in a box, and quantization. Thank you!!
I have seen a lot of videos on the Schrodinger Equation, but this video brings them all full circle, 2 pi radians :) Lots of details, great job! A compliment from Mr Ash says it all.
I like how you don't just explain how great is Schrodingers equation and But you really give them a feel of how Schrodingers equation actually work.great job👍👍
Hi Parth, I feel compelled to say what an absolutely BRILLIANT job you do in explaining each lesson. I have been a secondary teacher for some 40 or so years; I marvel are your style. You are a 'natural'. Whatever you do, don't change a thing.
I love how you explained the connection between quantization and the usage of radians in the mathematics. Professors and books tend to skip over those aspects assuming it's trivial. Thanks for the help!
Exactly. In simplistic terms, the most probable locations of the electrons are like three dimensional standing waves. The first energy level has only one type of region, called an s-orbital, which is essentially spherical. The second energy level allows for both the s-orbital and a more complex set of regions called p-orbitals. Remember that these are regions of space where the probability of finding the electron is high, not absolute boundaries.
This is why some scientists have the theory that we leave in a matrix. Because the only way to simule our universe is quantizing energy it means the most basic form of energy in the universe have finite states.
"x + y = z." The equation "x + y = z" is a simple algebraic equation. To solve for one of the variables, you'll need to isolate it on one side of the equation by subtracting or adding the same value to both sides. For example, if you want to solve for x, you would subtract y from both sides: x + y = z y - y x = z - y So now you know that x = z - y. You can plug in any values you have for z and y to find the corresponding value of x. I hope this helps. Yes, it can be challenging for teachers to manage students who do not study or listen in class.
Decades back, as part of an admissions procedure to a graduate physics course, i had to write a term-type paper on the Schrodinger wave equation. About which, as a humble pure mathematician, I knew nothing. It took me a week's hard work. If I could have seen your video, it'd have taken me a lazy afternoon! (Yes, my efforts persuaded the admissions committee!) I now always refer people to your videos if hey want a very clear explanation of basic (not the same as simple!) points in physics.Thanks, Parth - from all your happy customers!
You just explained to me in 13 minutes what my prof couldn’t in two weeks. Please do a video just like this for the time-dependent Schrödinger equation.
Hey man thanks for the videos, you describe these in a simple comprehensive way. Sometimes I have a hard time describing some of the stuff to people. Because as you know it can get very convoluted. I like your videos Man.
Really nicely explained, thank you. Just a little technicality at the end when you said that the wave function "is the probability", it's not actually : the wave function is the probability amplitude, the squared modulus is the probability density, and the squared modules times "dx" (or d^N.r N being the dimension) is the actual probability.
This is the absolute best explanation of solving this equation! Thank you so much and I will be referring to this in my upper level physics classes for my major ☺️
You are the best at explaining such complicated topics. I can almost pretend that I understand what you are talking about. In other words, the probability that I can understand this stuff when I watch your videos is very high.
Thank you, Parth. I remember struggling mightily with the purpose of studying trigonometry. What my instructors failed to mention was how essential it would be to understanding the nature of the universe.
You are a great teacher!!. This is the best introduction to solve the schordinger equation anyone can find. It amazes me how brillant was schrodinger in oder to write this elegant equation that is hable to describe an infinite number of possible scenarios.
You mean just like the probability of roughly 1/6 describes the likelihood of a particular outcome of a dice throw? What's amazing about that? The probability distribution doesn't tell you anything specific about the dice and their dynamics.
@@helmutalexanderrubiowilson6835 Not all that much. He came up with an unphysical equation that is one step above Bohr's model of the atom. The real theory is quantum field theory.
Ohhh!!! Love it... This video made more sense because I just studied the chapter Waves, so I could relate quantization to the overtones or harmonics in waves that are restrained between two walls.
See a wave restrained has a minimum frequency which we call the fundamental frequency as if we draw the displacement curve we see that the wavelength λ is related to the length as λ/2 = L So the fundamental frequency would be f = v/2L I was referring that.😊
@@mobizoid2571 right, but at 10:50 Parth says the particle can only have specific energies, and then look at the guitar string: it doesn't have a specific frequency. Instead it's a mix of many from a series. Explain.
@@DrDeuteron yeah so... At first wasn't actually relating a wave to a guitar wave right? Sir, you mentioned a guitar which I guess you have used a guitar before... So I am trying to mould my explanation into you example... Let's consider this case... It's a hypothetical guitar... Forget the sweet sounds that an actual guitar makes... Think theoretically, suppose you give the guitar so little energy that It only has one anti-node between the endings (i.e.nodes) this is the fundamental energy, you can not go lower than this, Now the difference between energies of a guitar string owing to the large length are so less that we may not be able to notice it... However after having a wave frequency of v/2l we physically cannot have a frequency of 3v/4l for that particular string... We have to have v/l which is the second harmonic right? However the length of the string is soo high and the mass per unit length is soo low that the energy difference is not noticed however we cannot cease it's existence also I am talking about one string not combination of different strings vibrating. 😊
@@DrDeuteron Actually mobizoid analogy is very accurate to the particle in a box scenario. A guitar string fixed at both ends similarly to particle to a box cannot oscillate at any frequency infact the length of the string and the two fixed ends constraints the string to produce standing waves of Harmonics only (Either odd or even) which is similar to the particle in a box scenario. But here the reasons are due to the quantum nature of the particle and there they are due to waves interference pattern. Infact normal audio waves and other signals (which are described in waves) also exhibit Heisenberg's uncertainity principal through the fourier transforms. So actually the wave analogy was fiting.
How the Schrodinger Equation is actually used is a concept that always escaped me until now. Thank you for a fantastic explanation as well as for not shying away from more advanced concepts like derivatives and radians. Subscribed.
I'm eagerly waiting for your video on Bose Einstein condensate 😀 By the way I've not seen the video yet but I can surely say that it will be wonderful 😊❤️
I badly want to know how did you gain such a conceptual initiative understanding of all different areas in physics in the first place!! Please make a video on how to understand physics like you!!! Kudos 🙏🙏
It takes hard work, a lot of study time, and good teachers. Most importantly, remember that physics is not just a set of equations to be solved, it is the study of the real world, and each equation tells one something about an aspect of it. I always tried to teach my students the concepts behind the equations before teaching the equations. Understanding the concept is a powerful tool because it allows you to not only recreate equations as you need them (effectively making them intuitive), but give you an insight into the beauty of the processes that govern the real world.
@@wayneyadams Physics sounds easy when you have to solve differentitation and integration questions since childhood along with other maths problems, its a trend in Indian families, they make there kids do that and anyone with weak maths is automatically considered dumb and a faliure, not much is expected out of them, the mission of every indian child since birth is to crack Neet or IIT's so you have to either be very good at maths and physics or chemistry and biology and with the amount of population we have, its literally a cut throat competition hence parents start preparing kids since childhood cause ending in an IIT and good Medical college means massive wealth and social respect.
Excellent! I am trying to correlate this with the Standing waves - we see the nodes (and antinodes) at specific frequencies. I am trying to make a toy for my kids, with electric motors at the ends of a string, wiggling it to form a standing wave. The potential difference across the motors (which directly corresponds to the energy of the particles of the string) and the RPM of the synchronized motors (which directly correspond to the frequency of the wave) are in quantized values for the multiples of the nodes to form.
Yes, the correlation between the Schrödinger equation and standing waves is related to the quantization of energy levels. In the case of a string, the standing wave pattern forms at specific frequencies, with nodes and antinodes corresponding to specific energy levels. By adjusting the RPM of the motors, you can control the frequency of the wave and therefore the energy levels of the particles in the string. This relationship between energy and frequency is governed by the Schrödinger equation. In your toy, the potential difference across the motors represents the energy of the particles, and the RPM of the motors represents the frequency of the wave, both of which are quantized for the formation of standing waves. Please send your Toy to me in the mail. lol
The Schrödinger equation is a partial differential equation that describes the time evolution of a quantum mechanical wave function. Solving the Schrödinger equation for a specific system can be quite challenging and often requires numerical methods. Here's an example of how you can solve the time-independent Schrödinger equation for a simple one-dimensional potential using Python: import numpy as np from scipy.integrate import solve_bvp def Schrödinger(x, psi, E): return np.array([psi[1], 2*(E-V(x))*psi[0]]) def V(x): return 0.5*x**2 def boundary_conditions(ya, yb): return np.array([ya[0], yb[0]-1]) x = np.linspace(0, 1, 25) E = 0.5 psi_init = np.zeros((2, x.size)) psi_init[0] = 1 res = solve_bvp(Schrödinger, boundary_conditions, x, psi_init, args=(E,)) print(res.message) print(res.success) This code uses the solve_bvp function from the scipy.integrate module to solve the Schrödinger equation for a given energy E. The function Schrödinger takes in the position x, the wave function psi, and the energy E and returns the derivatives of the wave function. The potential V is defined as a simple harmonic oscillator potential in this example. The boundary conditions are set so that the wave function approaches 1 at one end of the position range. The res object returned by solve_bvp contains the solution of the Schrödinger equation and information about the solution process.
I wish you were my Quantum Physics teacher... my teacher is an old guy getting ready to retire and doesn't care at all, I have to watch your videos to actually learn what he attempts to present in the class.
I apologize for my comments (immediately below) from yesterday. I was 100% wrong. It is clear that "a" is the right hand boundary of the box. Your videos are fabulous.
Parth - love your videos! You are a gifted teacher. TOPIC SUGGESTION - please show us how symmetry is really used by physic to manipulate an equation or limit the scope of alternative answers to an equation. There are tons of videos "explaining" symmetry as something "symmetrical" but not on how symmetry comes into play in the way physicists use symmetry in calculated expected values, or solve equations, etc.
Congratulations. The video is excellent. I would just like to make a comment: it is preferable to say that the wave function allows calculating the probability of finding the particle in a "region", and not at a "point". in fact, for a wavefunction that is not shaped like a Dirac's delta, the probability of finding the particle at a specific point is always zero. Your videos are always very good.
Wonderful. I wish I had this in 1968 when I took quantum physics. I was hoping you would arrive at a psi as a complex number to help explain how S's eqn gives complex number solutions
Remember that second order differential equations also have exponential solutions in powers of i (imaginary number). He could have solved the equation that way, but using sine makes it easier to visualize and understand the solution, because we can all understand what a sine curve looks like. If you want an exponential just use this definition of sin. sin(x) = 1/2i (e^ix - e^-ix)
This was extremely helpful! I’m a junior physics major and I’m taking my qualification exam tomorrow to be allowed to write a thesis in physics, and this is a really helpful explanation and refresher for the quantum mechanics part of the exam
Sir what job you do? I want to do a physics degree but I am sacred as I can see that there are not a good employment rates for physicists and the salary for them is also very low. But I LOVE physics. So please tell me what job can I have if I want to be a physicist? Googling this gives me bunch of gibrish
@@colewalker2916 and science also has no use without money. If you have money you will be able to buy the equipment to test out different things. I think the biggest problem is that physics tells us the theory but for most of us, we feel that learning the theory is enough. No it is not. If you can apply it to prove something, or to make something more efficient, then it will be the correct use of physics. Not just learning concepts of physics and do nothing for the rest of the life. Lol I am not trying to act rude btw though. But it is the truth, isn't it? What's the point of learning all these amazing things when you cannot make something amazing using the things e.g. a robot. Most of the physics jobs are teachers. For me, it is WHAT? Why?
The wave function describes the behavior of an infinite number of repetitions of the same experiment, while a state describes the actual measured behavior of one experiment. Think of the wave function as an entity similar to a probability distribution. The probability distribution can't tell us what number an individual dice throw will generate, but it can tell us that, on average, all numbers will be equally likely.
The visual approach is very appealing, thanks! A little remark: The guy was called Erwin SchrÖdinger, not "Schrodinger" ;). An ö ≠ o, completely different letter.
sir thank you.In this semester i'm studying Solid state Physics. But i didn't complete QM. but A little bit QM is needed for SSP. that's why i need to understand Schrodinger equation. And your video was too much helpful.
8:08 but even with the condition that ψ(0) = ψ(a) = 0, ψ is still not differentiable at the endpoints, so I don't get whats the point of these conditions
The differentiability does not matter exactly at the boundaries in this case - they do matter 'dx' from the boundaries, and within the region. Of course, this a theoretical system, with assumptions on the boundaries - which is an attempt to make mathematics simple and easy to understand. This would never be a practical scenario.
Excellent episode! Masterful explanation of a very difficult topic. Couldn't have done it better myself. I won't need to make a video on this topic, as I will just refer people to yours. Ha.
Arvin you're a legend, thank you for such a wonderful compliment!
You're both great, I love watching your videos
😀
Finally here comes my favorite youtubers.
Wait what arvin ash is here
I think a combination of you and up and atom and 3 blue 1 brown doing a deep dive into quantum mechanics to possibly the best series ever created
Add some apostrophes to names bro
bro. that would be incredible
right, or he could just rise on his own since hes good enough to attempt that himself, and not have his efforts accredited to them
All my TH-cam recommendations are videos made by Parth😁😁🤩
Haha thank you so much for your support :D
You're brilliant. Clearest explanation of this I've seen. I love how you didn't really assume any prior knowledge and explained every step; this was just what I needed.
this was more than a clear explanation, he took the arrogant-physics-genius-higher-intelligence-explanation ingredient that's baked into learning physics, out
This is one of my favourite channels! Tysm😭❤️
PARTH ROCKS LIKE ALWAYS!😎
U r from India I guess
It's ur dream to be at NASA
@@localtitans4166 LoL I think it's related to quantum physics not astronomy
Phys Major here, really glad you posted this. just shows whats up ahead for me in junior year. The walk-through was good, really. Makes one excited for their 1st QM course.
Wish we had a resource like this back in my day. We were chucked in straight at the deep end with heavy-duty bra-ket notation, operators and the rest of it. Needless to say, I never got a good qualitative understanding and grounding in of QM, and essentially had to blag my way through the remainder of my course.
You Sir are extremely talented. This is probably the clearest, most elegant description of solving the wave equation I have ever seen uploaded to TH-cam. Congratulations!
Studied Chemistry in the second half of the 80´s. Phyiscs and this topic was also part of it. We solved it for Hydrogen. It was really fun (no sarcasm). But still today (around + 35 years later) I could´nt get my head around the fact that time has to be eleminated / ignored in the first step. Seems to me that time does does not exists. Waiting for someone who figures out that the dimensions are curled one quantum level and that this is the reason why we experience time, the (non-force) effect of gravity, black matter and energy and strange things, like time bending, when "we go closer" to (massive) objects / black holes ... Pretty sure some one will find out that black holes are not singularities. Black holes are the oposite. Starting with the event of horiziont the dimension are so far "un-curled" (= straight) that (from our point of view) we could not "see" beyond our > 3 dimensions because at this point there are way more dimensions. So black holes aren´t holes they are the opposite, they are columns. lol . greek mythology came in my mind ... Didnt they say that the world is carried by Atlas and columns?
I’m in modern physics 2 and we deal with the Schrödinger equation all the time. This is the best and most concise explanation of the Schrödinger equation, boundary conditions, particle in a box, and quantization. Thank you!!
This is probably the most succinct and intuitive way I've heard the particle in a box explained :)
I am a 12 grader with chemistry exam in 6 days, its 1.30 am..... why am I here instead of completing valance bond theory?
I have seen a lot of videos on the Schrodinger Equation, but this video brings them all full circle, 2 pi radians :) Lots of details, great job! A compliment from Mr Ash says it all.
I like how you don't just explain how great is Schrodingers equation and But you really give them a feel of how Schrodingers equation actually work.great job👍👍
Hi Parth, I feel compelled to say what an absolutely BRILLIANT job you do in explaining each lesson. I have been a secondary teacher for some 40 or so years; I marvel are your style. You are a 'natural'. Whatever you do, don't change a thing.
Love your videos dude! 🤘
I love how you explained the connection between quantization and the usage of radians in the mathematics. Professors and books tend to skip over those aspects assuming it's trivial. Thanks for the help!
i love this man, i waited from 9:00am (IST) till 9:30 pm (4:00pm UK time ) to watch his vids
Thanks very much for your support!
Me after studying atomic physics in high school:
Same here,After Studying Atomic Structure of 11th Grade
Which country r u from bro @@ArifHossain-ou9oe
@@Aahaanrai7010 from India ig. We have atomic structure in class 11
thanks a lot. I'm a computer scientist and haven't studied physics for 7 years. but everything was explained so well that I was able to understand.
Is this why electrons fall into specific energy levels, due to their wave functions having discrete energies?
Exactly. In simplistic terms, the most probable locations of the electrons are like three dimensional standing waves. The first energy level has only one type of region, called an s-orbital, which is essentially spherical. The second energy level allows for both the s-orbital and a more complex set of regions called p-orbitals. Remember that these are regions of space where the probability of finding the electron is high, not absolute boundaries.
@@wayneyadams Very intersting, thank you
This is why some scientists have the theory that we leave in a matrix. Because the only way to simule our universe is quantizing energy it means the most basic form of energy in the universe have finite states.
You made it look easier than what I thought, thx for the effort!
At school my teachers never told me how to solve the equation..... Thanks for this video..... ❤️
I mean, that's not what they're supposed to teach you in school anyways.
"x + y = z."
The equation "x + y = z" is a simple algebraic equation. To solve for one of the variables, you'll need to isolate it on one side of the equation by subtracting or adding the same value to both sides.
For example, if you want to solve for x, you would subtract y from both sides:
x + y = z
y - y
x = z - y
So now you know that x = z - y. You can plug in any values you have for z and y to find the corresponding value of x.
I hope this helps. Yes, it can be challenging for teachers to manage students who do not study or listen in class.
Decades back, as part of an admissions procedure to a graduate physics course, i had to write a term-type paper on the Schrodinger wave equation. About which, as a humble pure mathematician, I knew nothing. It took me a week's hard work. If I could have seen your video, it'd have taken me a lazy afternoon! (Yes, my efforts persuaded the admissions committee!) I now always refer people to your videos if hey want a very clear explanation of basic (not the same as simple!) points in physics.Thanks, Parth - from all your happy customers!
You just explained to me in 13 minutes what my prof couldn’t in two weeks. Please do a video just like this for the time-dependent Schrödinger equation.
This was such a good explainer I could actually guess the next step and do all the maths myself!!!
Hey man thanks for the videos, you describe these in a simple comprehensive way. Sometimes I have a hard time describing some of the stuff to people. Because as you know it can get very convoluted. I like your videos Man.
Sir, you are getting better and better each lesson.. Thank you so much!
Really nicely explained, thank you. Just a little technicality at the end when you said that the wave function "is the probability", it's not actually : the wave function is the probability amplitude, the squared modulus is the probability density, and the squared modules times "dx" (or d^N.r N being the dimension) is the actual probability.
This is the absolute best explanation of solving this equation! Thank you so much and I will be referring to this in my upper level physics classes for my major ☺️
Best video on youtube on Schrodinger eqn❤
You are the best at explaining such complicated topics. I can almost pretend that I understand what you are talking about. In other words, the probability that I can understand this stuff when I watch your videos is very high.
This is the best explanation on the basics of the SE I've come across.
Your Videos are by far the best Physics Videos out there mate!! Ur vids are the main ones which pop up in my recommendations Thx a lot!!
Extremely lucid discussion on an otherwise unwieldy topic, thank you Parth G! Also your footnotes are hilarious 👍👍👍
Thank you, Parth. I remember struggling mightily with the purpose of studying trigonometry. What my instructors failed to mention was how essential it would be to understanding the nature of the universe.
Parth , you are the best Physics "explainerer’ on the web! I need to watch all your videos now.
Very brief explanation THANKS ...!! please dirac equation next ?
You are a great teacher!!. This is the best introduction to solve the schordinger equation anyone can find. It amazes me how brillant was schrodinger in oder to write this elegant equation that is hable to describe an infinite number of possible scenarios.
You mean just like the probability of roughly 1/6 describes the likelihood of a particular outcome of a dice throw? What's amazing about that? The probability distribution doesn't tell you anything specific about the dice and their dynamics.
@@schmetterling4477 really? so schrodinger didn't do anything special for you?
@@helmutalexanderrubiowilson6835 Not all that much. He came up with an unphysical equation that is one step above Bohr's model of the atom. The real theory is quantum field theory.
You’re absolutely unbelievably knowledgeable!
Woah....this was amazing
There's a request: can you make a detailed video on DIRAC HOLE THEORY??
Best Physics explanaior and the best TH-cam channel for Physics in whole TH-cam .
Thanks a bunch! You made it comprehensible enough for a non-physicist layman.
Ohhh!!! Love it... This video made more sense because I just studied the chapter Waves, so I could relate quantization to the overtones or harmonics in waves that are restrained between two walls.
but a wave on a guitar string doesn't have a definite frequency.
See a wave restrained has a minimum frequency which we call the fundamental frequency as if we draw the displacement curve we see that the wavelength λ is related to the length as λ/2 = L
So the fundamental frequency would be f = v/2L
I was referring that.😊
@@mobizoid2571 right, but at 10:50 Parth says the particle can only have specific energies, and then look at the guitar string: it doesn't have a specific frequency. Instead it's a mix of many from a series. Explain.
@@DrDeuteron yeah so... At first wasn't actually relating a wave to a guitar wave right?
Sir, you mentioned a guitar which I guess you have used a guitar before... So I am trying to mould my explanation into you example...
Let's consider this case... It's a hypothetical guitar... Forget the sweet sounds that an actual guitar makes... Think theoretically, suppose you give the guitar so little energy that It only has one anti-node between the endings (i.e.nodes) this is the fundamental energy, you can not go lower than this,
Now the difference between energies of a guitar string owing to the large length are so less that we may not be able to notice it... However after having a wave frequency of v/2l we physically cannot have a frequency of 3v/4l for that particular string... We have to have v/l which is the second harmonic right?
However the length of the string is soo high and the mass per unit length is soo low that the energy difference is not noticed however we cannot cease it's existence also I am talking about one string not combination of different strings vibrating. 😊
@@DrDeuteron Actually mobizoid analogy is very accurate to the particle in a box scenario. A guitar string fixed at both ends similarly to particle to a box cannot oscillate at any frequency infact the length of the string and the two fixed ends constraints the string to produce standing waves of Harmonics only (Either odd or even) which is similar to the particle in a box scenario. But here the reasons are due to the quantum nature of the particle and there they are due to waves interference pattern. Infact normal audio waves and other signals (which are described in waves) also exhibit Heisenberg's uncertainity principal through the fourier transforms. So actually the wave analogy was fiting.
Loved your patient description of what happens "at the walls". It leads naturally to the periodic solutions.
How the Schrodinger Equation is actually used is a concept that always escaped me until now. Thank you for a fantastic explanation as well as for not shying away from more advanced concepts like derivatives and radians. Subscribed.
This channel is on a whole new level 🙏
Hats off to you sir.
This video is a must for someone who just started learning the Schrodinger equations. Amazing explanation
Parth you are really a physicist........
Just take our lecture the next Tuesday!😎
I'm eagerly waiting for your video on Bose Einstein condensate 😀
By the way I've not seen the video yet but I can surely say that it will be wonderful 😊❤️
Beautiful explanation!! The step-by-step development of the theory is really awesome!
I wish I could give more than one like to your video, man. Awesome result, you are an amazing teacher.
I think that this is your best video that i have watched
I just discovered this channel. I feel like i have to watch all his old videos from scratch now!
Excellent video. Very interesting, informative and worthwhile video.
Sir, this was nothing short of genius
*As always, an incredible explanation. You simplified a complex looking expression. Great job.*
Bro, I took 3 quantum mechanics classes, and you explained everything far better in 13 minutes.
I badly want to know how did you gain such a conceptual initiative understanding of all different areas in physics in the first place!! Please make a video on how to understand physics like you!!! Kudos 🙏🙏
It takes hard work, a lot of study time, and good teachers. Most importantly, remember that physics is not just a set of equations to be solved, it is the study of the real world, and each equation tells one something about an aspect of it. I always tried to teach my students the concepts behind the equations before teaching the equations. Understanding the concept is a powerful tool because it allows you to not only recreate equations as you need them (effectively making them intuitive), but give you an insight into the beauty of the processes that govern the real world.
@@wayneyadams Physics sounds easy when you have to solve differentitation and integration questions since childhood along with other maths problems, its a trend in Indian families, they make there kids do that and anyone with weak maths is automatically considered dumb and a faliure, not much is expected out of them, the mission of every indian child since birth is to crack Neet or IIT's so you have to either be very good at maths and physics or chemistry and biology and with the amount of population we have, its literally a cut throat competition hence parents start preparing kids since childhood cause ending in an IIT and good Medical college means massive wealth and social respect.
I can't believe I actually understood that. Amazing teacher!
Excellent! I am trying to correlate this with the Standing waves - we see the nodes (and antinodes) at specific frequencies. I am trying to make a toy for my kids, with electric motors at the ends of a string, wiggling it to form a standing wave. The potential difference across the motors (which directly corresponds to the energy of the particles of the string) and the RPM of the synchronized motors (which directly correspond to the frequency of the wave) are in quantized values for the multiples of the nodes to form.
Yes, the correlation between the Schrödinger equation and standing waves is related to the quantization of energy levels. In the case of a string, the standing wave pattern forms at specific frequencies, with nodes and antinodes corresponding to specific energy levels. By adjusting the RPM of the motors, you can control the frequency of the wave and therefore the energy levels of the particles in the string. This relationship between energy and frequency is governed by the Schrödinger equation. In your toy, the potential difference across the motors represents the energy of the particles, and the RPM of the motors represents the frequency of the wave, both of which are quantized for the formation of standing waves.
Please send your Toy to me in the mail. lol
omg I kind of understand Schrodinger Equation now after 3 year of reading .... thank you!
Taking quantum mechanics this quarter, so excited!
You do such a great job with concepts. And I don't know anyone who communicates "the joy of physics" better. Kudos Parth!
I have no clue why was this in my news feed, watched it anyways, gj on this one, subbed
I am addicted to physics and this channel ❤️❤️
Nice and clean explaination!
Thanks Parth - I always wanted to understand how to solve the SE, now you made it easy to understand.
AMAZING. Wow really intuitive. Thanks!
Great video! Amazing job. The world needs more of these explanations.
The Schrödinger equation is a partial differential equation that describes the time evolution of a quantum mechanical wave function. Solving the Schrödinger equation for a specific system can be quite challenging and often requires numerical methods. Here's an example of how you can solve the time-independent Schrödinger equation for a simple one-dimensional potential using Python:
import numpy as np
from scipy.integrate import solve_bvp
def Schrödinger(x, psi, E):
return np.array([psi[1], 2*(E-V(x))*psi[0]])
def V(x):
return 0.5*x**2
def boundary_conditions(ya, yb):
return np.array([ya[0], yb[0]-1])
x = np.linspace(0, 1, 25)
E = 0.5
psi_init = np.zeros((2, x.size))
psi_init[0] = 1
res = solve_bvp(Schrödinger, boundary_conditions, x, psi_init, args=(E,))
print(res.message)
print(res.success)
This code uses the solve_bvp function from the scipy.integrate module to solve the Schrödinger equation for a given energy E. The function Schrödinger takes in the position x, the wave function psi, and the energy E and returns the derivatives of the wave function. The potential V is defined as a simple harmonic oscillator potential in this example. The boundary conditions are set so that the wave function approaches 1 at one end of the position range. The res object returned by solve_bvp contains the solution of the Schrödinger equation and information about the solution process.
Thanks for this video. Well done! Will be back for additional videos going deeper!
That’s great video you make everything easier to understand thank you brother. Would you please do Fourier transform ?
Good job with the timestamps
your video gave me an MIT ad!!!
Amazing!
I finally understand normalization. Thank you
Discovered ur channel and oh my! Loveee it!!!! ❤❤❤
I wish you were my Quantum Physics teacher... my teacher is an old guy getting ready to retire and doesn't care at all, I have to watch your videos to actually learn what he attempts to present in the class.
"Solid ass walls." I love it. Great videos 🤓👍
I apologize for my comments (immediately below) from yesterday. I was 100% wrong. It is clear that "a" is the right hand boundary of the box. Your videos are fabulous.
Finally I understood that! Thank you soooo much 😭
Parth - love your videos! You are a gifted teacher.
TOPIC SUGGESTION - please show us how symmetry is really used by physic to manipulate an equation or limit the scope of alternative answers to an equation. There are tons of videos "explaining" symmetry as something "symmetrical" but not on how symmetry comes into play in the way physicists use symmetry in calculated expected values, or solve equations, etc.
Congratulations. The video is excellent. I would just like to make a comment: it is preferable to say that the wave function allows calculating the probability of finding the particle in a "region", and not at a "point". in fact, for a wavefunction that is not shaped like a Dirac's delta, the probability of finding the particle at a specific point is always zero. Your videos are always very good.
Wonderful. I wish I had this in 1968 when I took quantum physics. I was hoping you would arrive at a psi as a complex number to help explain how S's eqn gives complex number solutions
Remember that second order differential equations also have exponential solutions in powers of i (imaginary number). He could have solved the equation that way, but using sine makes it easier to visualize and understand the solution, because we can all understand what a sine curve looks like. If you want an exponential just use this definition of sin.
sin(x) = 1/2i (e^ix - e^-ix)
This person is really genius
This was extremely helpful! I’m a junior physics major and I’m taking my qualification exam tomorrow to be allowed to write a thesis in physics, and this is a really helpful explanation and refresher for the quantum mechanics part of the exam
❗️Excellent explanation❗️
Wonderful explanation!
Really simple and usefuel af. Love the videos, subbed
Sir what job you do? I want to do a physics degree but I am sacred as I can see that there are not a good employment rates for physicists and the salary for them is also very low. But I LOVE physics. So please tell me what job can I have if I want to be a physicist? Googling this gives me bunch of gibrish
Be an engineer
@@mzflighter6905 lol
You don’t go into science for the money
@@colewalker2916 and science also has no use without money. If you have money you will be able to buy the equipment to test out different things. I think the biggest problem is that physics tells us the theory but for most of us, we feel that learning the theory is enough. No it is not. If you can apply it to prove something, or to make something more efficient, then it will be the correct use of physics. Not just learning concepts of physics and do nothing for the rest of the life.
Lol I am not trying to act rude btw though. But it is the truth, isn't it? What's the point of learning all these amazing things when you cannot make something amazing using the things e.g. a robot. Most of the physics jobs are teachers.
For me, it is WHAT? Why?
@@arnoahmed9269 calm down
You're so good at this. I would love to see something like this that really explains how the wave-finction is related to the vectors in state-space
The wave function describes the behavior of an infinite number of repetitions of the same experiment, while a state describes the actual measured behavior of one experiment. Think of the wave function as an entity similar to a probability distribution. The probability distribution can't tell us what number an individual dice throw will generate, but it can tell us that, on average, all numbers will be equally likely.
this was super helpful, thank you so much!
The visual approach is very appealing, thanks! A little remark: The guy was called Erwin SchrÖdinger, not "Schrodinger" ;). An ö ≠ o, completely different letter.
sir thank you.In this semester i'm studying Solid state Physics. But i didn't complete QM. but A little bit QM is needed for SSP. that's why i need to understand Schrodinger equation. And your video was too much helpful.
God! With that video you got my subscription! Excelent explanation!
Great, high quality video. Big thanks from an intro to quantum student
8:08 but even with the condition that ψ(0) = ψ(a) = 0, ψ is still not differentiable at the endpoints, so I don't get whats the point of these conditions
The differentiability does not matter exactly at the boundaries in this case - they do matter 'dx' from the boundaries, and within the region. Of course, this a theoretical system, with assumptions on the boundaries - which is an attempt to make mathematics simple and easy to understand. This would never be a practical scenario.
Best explanation ever!
Best video yet
Best explanation so far 🙏
Thank you so much
The amount of effort in this video my gosh
Finally understand why an electron can't fall into the nucleus, but plz provide some mathematical solutions/solving