Introduction to Quantum Mechanics: Schrodinger Equation
ฝัง
- เผยแพร่เมื่อ 24 ธ.ค. 2017
- There's no better way to celebrate Christmas than with a 12 minute video on the Schrodinger Equation! In this lesson, I introduce Quantum Mechanics with a discussion on wavefunctions and the Schrodinger Equation (in 1-D). I show how wavefunctions can represent probability density functions (via the norm-squared), and discuss the significance of this representation.
I then introduce/revisit some basic Statistics concepts, and end the video with a proof of how the normalization of wavefunctions stays preserved with time.
Questions/requests? Ask in the comments!
Prereqs: This whole playlist: • Quantum Mechanics: Mat...
Lecture Notes: drive.google.com/open?id=1IA_...
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Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
NOTE: At around 11:30-11:45, I mention how the 'boundary' integrals have to approach zero at +/- infinity. This is true for square-integrable functions that come up in Physics. However, as one of the commenters pointed out, there are exceptions (i.e. square-integrable functions that don't approach zero at infinity). These exceptions aren't found in Physics though, so we'll ignore them, but I figure they're worth mentioning as a footnote.
In korea now, due to covid19 many universities are taking lectures online. (TH-cam uploaded lecture, lectures using zoom meating, etc) and you are much better than my professor.
ㅇㄱㄹㅇ
No one cares about Korea
i hate online lectures when teachers oblige students. i like liberated learning though
@@amarelli9304 please stay positive
@@natashanonnattive4818 no
Thank you for referring to Quantum Mechanics as "not very difficult" and "not very different", it kinda takes away the chills that I get thinking about this subject :)
I've been on the lookout for precise videos like this, and this is THE BEST i have found! It's so easy to understand, the derivation is done in detail without missing any steps. Being a biology student, i'm taking a stat phy course to get a better understanding of the quantum world. The math wasnt that hard. Students are very intimidated by professors teaching this subject. The way you treat this as something that's not complex but can be understood in parts and with different viewpoints is encouraging!
This sounds to me like someone created a Text to Speech based on Khan's voice!
Maybe they did....
You think Khan wants do all this all himself?
that's so creepy
I legitimately cannot tell if it is a human talking or a computer. On one hand, it would take a lot of effort to feel a script into a computer and have it sound so good. On the other hand, it might amaze me more that there is an actual person in the world who has such an odd cadence.
@@forrestkennedy5458 After listening again I think it could be some audio compression artefacts paired with a flat delivery. It sounds like the kind of speech patterns you would use when using some kind of recognition software. I agree that text to speech isn't there yet, but I'm surprised how good it has got in the last couple of years. It's nearly over the uncanny valley in my opinion.
No, it's less laid back and It's a lot better
Thank you so much, sir.
Your video is clear cut as always and direct.
The explanation is definitely great.
Thanks in million.
No problem! Thank you for the kind words!
Excellent way of explaining such a complex topic. Grateful. Thanks.
As always, awesome presentation Faculty of Khan! Thanks, and happy holidays. :)
Thank you and happy holidays!
My Classical Mechanics 'Glory Days?' LOL!
back when life more easy
this is a very good introduction to the Schrodinger equation !
Great job!
love these funny yet informative video, its like you're tricking me to learn without me knowing lol
You are the best teacher !
Amazing lecture!!
Crystal clear explanation thank you sir.
Although I only know basics physics, the explanation provided in this video gave a real understanding of the Schrodinger equation in less than 15 minutes. I am simply left speechless. Thank you so much for such an insightful video and for your genuine desire pass on your knowledge.
Glad I could help; I appreciate the kind words!
You don’t really need to go in-depth with many classical mechanics maybe basics and then some chem stuff but as long as you got up to calc 3 and differential eq you good bruv.
love it love it love it very clearly explained thank you
you are Rock sir, You helped me a lot in my Phsics course. Will You please make lectures on Perterbation theory and WKB approximation.
thx to this video!!!
utube is my real prof
You talk like robot, but your explanation is amazing. Thank you
excellent explanation
Good explanation
Thank you very much
Really enjoyed this video!
Glad you enjoyed it!
what a video
amazing thank you
More videos please!
great video, thank you.
No problem!
What are you using to create this video. Is there a certain package that you use?
Great video!
Thank you!
What are the parameters that we obtain from the Schrodinger equation?
I've come to learn about quantum mechanics after watching Oppenheimer
I see you are a man of culture!
Saying "measurement changes particle wave function," is entertaining. It's a very entertaining concept the more vague you remain. A more accurate statement would be that seeing requires photons and the photons hit the electrons and alter their motion. Any measurable thing that that you bounce off of the electron alters the motion of the electron. That's all it is. conservation of momentum...
Mashallah sir
Very nice explanation
'Preciate it.
But isn't the LHS of the schrodingers eqns a momentum operator on psi? How does that translate to total energy?
No, it's energy operator acting on the wave function in the LHS
I am confuse... its a great lecture, but Im gonna need to go back to calculus to learn some of these terms to understand it.
all i know is that it all checks out to one...
im a little bit confused with the Proof. to me It seems that u use the integration of psi sqr = 1 to proof the integration of psi sqr is a constant ? how can we understand about this auxiliary condition
Sir...I am not able to find the previous videos, it says server unreachable.
What tablet are you using?
More videos please
Thank you.
Just a remark, just because \psi is square integrable, that does not mean that it converges to zero. It means that if the function is uniformly continuous, but otherwise not.
Perhaps, one would argue that state functions that do not have \lim_{ |x| \to \infty } f(x) = 0 are not physical.
An example is the function f(x) = n on the interval [n, n+1/n^4). We then see that \int |f(x)|^2 dx = \sum_{n > 0} n^2/n^4, which is finite.
This f is not continuous, but one can (using smooth step functions instead of normal step function) find a smooth function that has the property that f(x) converges to infinity as x goes to infinity but is still square integrable.
Hi David, you are correct that being a square integrable function doesn't necessarily imply that \psi converges to zero at infinity. In fact, as I go back and re-read my books, the author mentions in one of the footnotes that there are square integrable functions which do not converge to zero at infinity, but that such functions are 'pathological' and 'do not arise in Physics'.
So for the purpose of these Physics lectures, I wouldn't worry too much about these unphysical exceptions. I will add a note to my description though; thank you for the comment!
I was just being pedantic. Thank you for the great material. :)
Haha it's fine. What you said is still useful.
question- are all probability density functions normalized?
im gonna request a video on Hamiltonian systems :) Would be nice if you could give examples like how Kepler problem is a hamiltonian system and how the wave function is too.
Sure, I'll add it to my to-do list!
Faculty of Khan how many things do you have on your to do list ?
Depends on what people are requesting. I'll probably go over Hamiltonian systems once I get further in my Nonlinear Dynamics series or Quantum Mech series, so there's probably quite a few videos in this series alone that I'd have to get through. I'm also working simultaneously on other series as well, so a rough estimate would be 20-30 more videos ahead of your request. Still, if there's a stronger push then I can move it ahead (which is what I did with Green's functions).
Faculty of Khan cool, take your time!
Waw, ok I have to first take my analysis 3 course to understand all of this I guess
At 11:07 I do not see any justification for cancelling the two integrals that have the strike-through lines in them. Also, the change in color from orange to white is confusing - why is it necessary. The newer terms in white are not a result of integration by parts..
just a normal 15 y/o girl being curious bout physics :D
@@bobbypederson That's completely irrelevant lol. We're all people interested in physics here
Hilbert Black you’ve made it relevant by actually acknowledging it ... stop shitting on 15 yo for no reason. Be delighted by curiosity in physics, not an ass
Bro who's gonna win the match between quantum
and relativity by the in
which university you
teach
I'm not sure if I can answer that question. There's too much *uncertainty* to say which will be *relatively* better.
11:35
This is false tho, there are many functions like sin(e^x) wich have finite integrals but don't have a limit. Do we just ignore these wavefunctions because they don't correspond to any real life scenario?
Hey, I really like your videos but somehow it is hard to have an overview of all the videos you have done. I think it would be good to classify all your video in playlists, and classify those playlists by topics. Now when I go under "playlists" on your channel, if I am interested in Quantum mecanics, I can't directly see all the videos you have made (for exemple there is not the playlist about the mathematical introduction to quantum mecanics).
Thank you Nicolas for the kind words and feedback! I have organized my videos into playlists and usually provide relevant links in the description: are they not visible to you?
@@FacultyofKhan Ok it's weird, because when I looked for the playlists on my Ipad I could find all of them, but with my laptop, I can't see all of them under the section "playlist" on your channel.
As good as any. Question: any reason why Faculty of Khan cannot pronounce Erwin's last name?
He's saying it right search it up.
@@RhysGirffiths
WeinSTEEN
FinkelSTEEN
Einsteen
GOH-del
SHROH dinger
search: how to search up
@@drake_sterlingEin-Stein. Goh-del. Schro-dinger.
@@drake_sterlingits different in areas so you're right and he's right. 😁
@@RhysGirffiths Yeah. you're right. foook,...
we ARE in another HEMISPHERE. aach.
Hmm but where does the Schrodinger equation come from? Can we derive it from basic principles?
yes, it's easy to derive, it comes from energy conversation .... want to know more about,,, fallow Leonard Susskind video lecture on quantum entanglement,,,, Sandford university ..
@reetanshu kumar Hmm okay. Thanks for the tip.
You can't really 'derive' it from a more fundamental principle. It looks similar to the principle of energy conservation, but the individual terms (e.g. the i*hbar*d/dt) don't really come from a particular place. In some ways, it's like Newton's Laws for Quantum Mechanics; it's a fundamental principle that doesn't come from anywhere - it just is (and it's worked so far experimentally).
@@FacultyofKhan u are right ,I learned more about it, in my Perturbation theory course, actually its comes from Schrödinger mind, its amazing..
@Faculty of Khan Ah but couldn't you argue that Newton's second law is actually empirical? The way I learned it, it can be derived from acceleration being directly proportional to the force applied and inversely proportional to the object's mass. That seems pretty straightforward.
I am probably missing something, but it seems that the explanation of the normalization proof is somewhat circular reasoning. In order for normalization to work psi and psi star must approach zero as x approaches infinity. If they dont then normalization does not work. Therefore psi and psi star approach zero as x approaches infinity?? Seems like, For A to be true, then B must be true, therefore B is true. I can see how conceptually psi star may approach 0 as x, distance, approaches infinity in the wave itself, , but idk seems like it also may not approach zero, may even become large.
idk please help
Excellent, but is the beginning of a series? Where is the next. Or was this the end. Hope not.
Here you go: th-cam.com/video/kUm4q0UIpio/w-d-xo.html
Better than Khan Academy
It's just the 1st chapter of Griffith's Intro to quantum mechanics
Well yes; Griffith's happens to be one of the best introductory books on the subject. That's why I've used it as the foundation for my series, though I follow a slightly different format because I've put the operator/math stuff in the beginning of my QM series.
Really good video, but the ads were kind of distracting and broke the flow
8:40 "because the particle has to be somewhere" sounds like a very bold assumption...
What's the use of studying a system that can not be found anywhere??? Like your god!
thank you, good video. Schrödinger has an "ö" (sometimes oe, if no "ö" available ), pronounced like peugeot, the car. Not so important.
wat an integral ?
String Theory was not a waste of time. Geometry is the key to Math and Physics.
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles?
Quantum Entangled Twisted Tubules: "A theory that you can't explain to a bartender is probably no damn good." Ernest Rutherford
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with the “Twistor Theory” of Roger Penrose? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Force" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Mesons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process.
Gamma photons are produced when a tube unwinds producing electromagnetic waves.
>>>>>>>>>>>>>>>>>>>>>>
Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. We know there is an unequal distribution of electrical charge within each atom because the positive charge is concentrated within the nucleus, even though the overall electrical charge of the atom is balanced by equal positive and negative charge.
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In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
>>>>>>>>>>>>>>>>>>>>>>>
How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
>>>>>>>>>>>>>>>>>>>>>>>>
Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
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They want kids to be LC and they deliver to Android schools! Coooool!
In bigger level nature operates on basis of newtons
equation of motion
but in quantum world or
in world of atoms nature
operates on schrodinge r
equqtion
It is Simple really
you did not change the wave function. You drew a statistical sample from it.
fi-NITE
The wave. Function of particles bass no physical meaning.There is no waving here.However remember that particles are prophages as if they are waves.Hence the square of the wave function gives the probability of finding the electron at that point.But the wave function has no Physical meaning.
Note
Waves are the ones whose mass has no physical meaning
Particles are the ones whose wavelength and frequency (and maybe wave function)have no physical meaning.
If you ask me " What exactly is waving here?" ,I'll reply/answer you "There is no waving here.".
Light is an intermediate between a particle and a wave.
Don't reply please I'm speaking with myself.
lol
Do you think it is logical that if the future is unfolding relative to the atoms, if we look down at the individual atoms we will find probability? This is an invitation to see a theory on the nature of time! In this theory we have an emergent uncertain future continuously coming into existence relative to the spontaneous absorption and emission of photon energy. Within such a process the wave particle duality of light and matter in the form of electrons is forming a blank canvas that we can interact with forming the possible into the actual! The future is unfolding with each photon electron coupling or dipole moment relative to the atoms of the periodic table and the individual wavelengths of the electromagnetic spectrum. As part of a universal process of energy exchange that forms the ever changing world of our everyday life the ‘past’ has gone forever. At the smallest scale of this process the ‘past’ is represented by anti-matter annihilation with the symmetry between matter and anti-matter representing the symmetry between the future and the past as the future unfolds photon by photon. In such a theory the mathematics of quantum mechanics represents the physics of ‘time’ with the classical physics of Newton representing processes over a period of time, as in Newton’s differential equations. In my videos I explain how this process is relative to temperature and the phase changes of matter.
Sounds like Steven Weinberg 2.0 ;-)
Einstein would disagree with all of this !
"God does not play dice with the universe!"
Einstein was just a very jealous boi
Neither would Schrodinger! The solution to the wave function can be a charge function, not a probability density function. Born asserted that it is a probability density function absolutely NO good physical justifications. Now this probability interpretation has led to all sorts of paradoxical experiment results that cannot be explained. And yet, they continue to use this probability interpretation of the wave function as if it is correct!
@@FacultyofKhan don't tell God what to do
_"Einstein would_ *_disagree with_* _all of this"_
Ol' Al *disagreed with himself!* Remember the infamous _"cosmological constant?"_
Bohr was right: you do not understand quantum mechanics if you do not find it shocking or utterly confusing. That's how I feel right now. Utterly confused.
Nevermind the quantum mechanics, how does he write so fast....
Lol, it’s just a sped up recording
You wouldn’t want to watch someone write this whole thing out in real-time
Nice, writing is a little sloppy and hard to read tho.
Can you please translate these videos into Arabic?
hadehhh, pusing saya Pak
Khan academy for physics
Make a website like khan or you should ask them to add your videos to the site! ❤️
make your video more and
more intuitive so one can
feel maths and physics
then you have millions of
subscribers I am sure
not that simple
How is any of this a true insight into reality and not a neat mathematical story?
What the fuck just happened
This is not an introduction lol when I was introduced none of this math was required to be introduced to it
As ever they are experts on all the mathematics, but physics? Poor, very poor. Normalisation is of no real importance. Should be left to the end, is of secondary importance. What does the equ. tell about the position of the particle? And why? This is of first order importance.