Before You Start On Quantum Mechanics, Learn This

Quantum mechanics is mysterious---but not as mysterious as it has to be. Most quantum equations have close parallels in classical mechanics, where quantum commutators are replaced by Poisson brackets. Get the notes for free here: courses.physic...
You can't derive quantum mechanics from classical laws like F = ma, but there are close parallels between many classical and quantum equations. Many fundamental quantum equations are expressed as a commutator of operators, such as the canonical commutation relation and the Heisenberg equation of motion. These equations have classical parallels where the quantum commutator is replaced by a classical operation called the Poisson bracket, up to a factor of i hbar. I'll show how Poisson brackets work, and how they mirror these key quantum equations.
Get all the links here: www.physicswit...
Intro to Lagrangian and Hamiltonian mechanics: • Lagrangian and Hamilto...
Introduction to the principle of least action: • Explaining the Princip...
Noether's theorem: • Symmetries & Conservat...
Tutoring inquiries: www.physicswit...
If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at / physicswithelliot , or make a one time contribution at www.physicswit.... Thank you so much!
About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswit....

[@pianophiliarmonic]

Your videos are crystal-clear, beautifully laid out and follow a precise progression, treating not so easy topics that are usually not well understood or explained with a lot of confusion. I think your videos are among the very top quality materials on physics divulgation, and I'm sure that more and more people will join. Keep up the excellent work!

[@PhysicswithElliot]

So glad you’re enjoying them! Thank you for the kind words!

[@masternobody1896]

@@PhysicswithElliot bro changed the board to black board it looks ugly

[@Manukapp]

@@masternobody1896 I like the blue board

[@hinglish7813]

I like the blue board

[@voidisyinyangvoidisyinyang885]

que Harold and the Purple Crayon on magnificent 8 mm in 1st grade!

[@shutupimlearning]

i love how your able to stay focused to the topic at hand to avoiding long tangents. It makes the videos so much easier to digest.

[@eigenchris]

I remember finding this connection between QM and CM really intriguing when I first learned it, but I'm also a bit sad that I've never learned a deeper reason for why the "replace Poisson brackets with commutators" rule makes sense. Do you know of any deeper algebraic or physical reason why this connection exists?

[@PhysicswithElliot]

Hi Chris, thanks again for sharing the video! The basic reason is that in quantum mechanics we want to represent classical functions like position and momentum as operators acting on the space of states. And we want that representation to respect the Poisson bracket structure that we started with, meaning that the commutator of operators satisfies the same relations as the Poisson bracket of the corresponding functions. But they can't literally be equal, because [\hat{x}, \hat{p}] has units of kg m^2/s, so we need a factor of \hbar to get the units right. And we want \hat{x} and \hat{p} to be Hermitian so that their eigenvalues are real, because those are the numbers we measure. But the commutator of two Hermitian operators is anti-Hermitian, so if it's going to be a constant it had better be a pure imaginary one, so we also need a factor of i. That gets us to [\hat{x}, \hat{p}] = i \hbar. There's other ways of getting at it, but hopefully that helps

[@debunkthis]

If u watch Lenny susskinds lectures on quantum mechanics he gives an explanation that’s quite satisfying I forget what lecture tho maybe 4-5.

[@eigenchris]

@@PhysicswithElliot Thanks. I'm curious what "other ways" there are. You can feel free to share links to other sources if it will save you time.

[@PhysicswithElliot]

Just as Hamilton's equation dx/dt = {x, H} determines how x changes with time, the Poisson bracket {x, p} determines an action of p on x by dx/da = {x, p} = 1. The solution is just x = x0 + a, where a is some arbitrary parameter, so that the action of p on x just shifts it over. We say that momentum is the generator of translations. In the quantum version, we look for a corresponding unitary operator U(a) that shifts the position operator by a constant: U^{-1}(a) x U(a) = x + a. Since U is unitary, we can write it as U(a) = e^{-i a p/\hbar} for some Hermitian operator p. Then at leading order in a this equation is (1 + i a p / \hbar)x(1 - i a p / \hbar) = x + a. The LHS is x - i a [x, p] / \hbar. Therefore [x, p] = i \hbar. This is the quantum version of the statement that p is the generator of translations in x.

[@eigenchris]

@@PhysicswithElliot Thanks. Strangely enough I was familiar with the quantum version of "momentum is the generator of translations" but not the classical version.

[@bartpastoor1028]

The quality and level of the videos is just too good and provide much insight. They seduce you to pick up a pen and paper to do the calculations yourself. I could not resist and am proud to have become one of your patreons just now. Keep up the good work!

[@PhysicswithElliot]

Thank you so much Bart!! Much appreciated!

[@liltike2197]

The only problem is that the hamiltonian is not always equal to the total energy.

[@musamoloi2149]

This is where the concept of spin (a form of angular momentum) gets weird as it has no classical counterpart that you can relate it to😍. I love physics.

[@bartpastoor1028]

Again very good. Yes I would appreciate to see Noethers Theorem worked out in Hamiltonian formalism.

[@pianophiliarmonic]

Me too!

[@PhysicswithElliot]

Thanks Bart!

[@nicolascalandruccio]

I'd like to see it too

[@nicolasbiscione8189]

I'd like too... : )

[@harritiainen3530]

Yes please thank you. Your videos are so simple to follow, thank you so much.

[@WildGamez]

PLEASE EXPLAIN. You have no idea how much researching I have done just to understand quantum mechanics. You are an absolute genius science educator. Keep up the good work man!!!!

[@PhysicswithElliot]

Glad it was helpful!

[@orangeguy5463]

From a mathematical perspective the commutator is famous in the context of Lie Algebras, an example of which is first order differential operators. Who knew that math was useful in physics?

[@Tyler-i2d]

Ya boi literally explained this in what took two weeks of lectures from my graduate classical mechanics professor. Very nice!

[@lengocchinh2339]

From Vietnam with love, thank you so much for clear and easy-to-understand video.

[@StrangestQuark2k]

As someone who is going to take QM in my next semester, thanks for the help! Thankfully we covered a lot of what you said in CM, but the video is a cool summary and refresher on the topic. Especially necessary when you have so many other subjects too.

[@PhysicswithElliot]

Glad it helped!

[@TheFreckCo]

As I'm going through my physics degree, this video is helping me a lot to better understand my classical dynamics course, thank you very much for these videos, I will follow up on your very useful video uploads.

[@volcanic3104]

My classical mechanics course glossed over hamiltonian mechanics, but your video was still very clear. Gonna go read up on hamiltonian mechanics now

[@jaimeduncan6167]

Men this videos are a jewel. You have a knack for explaining physics and it's clear that you put the effort into understanding the concepts and a lot of effort into this videos. Thanks for sharing. I hope the channel grows.

[@erichaag5229]

Yes, please do the more advanced explanation. If you have any experience with Bessel functions, I would like to see something on that. Really enjoy these videos!

[@PhysicswithElliot]

Thanks Eric!

[@APaleDot]

Wow, criminally underrated. I had to stop and absorb some of the mathematics at times because it moved so fast, but I understood everything. I really feel like my understanding of math and physics is leveling up.

[@PhysicswithElliot]

Excellent! Absolutely, ideally I’d suggest going through it again after you watch and working through the equations yourself to make sure everything clicks

[@r3lativ]

Definitely interested in the Hamiltonian version of Noether's theorem.

[@chriskindler10]

this is a really good and important place to start. especially for those who are interested in the theory since these concepts are also the cornerstone of quantum field theory. you could follow this up with a video about the interaction picture and other pictures

[@deepakjanardhanan7394]

Wowww... I press the like button at the middle of video itself. This is gem... Enlightening. Kindly put some intuitive videos of role of matrices in quantum mechanics. For eg: representing spin as matrices (Pauli matrices) etc..etc. If possible kindly make one video on Hamilton -Jacobi theory and transition to quantum mechanics....

[@PhysicswithElliot]

Thanks Deepak!

[@deepakjanardhanan7394]

@@PhysicswithElliot Waiting for your new uploads.

[@joevostoch8768]

They did not cover Lagrangians and Hamiltonians in my engineering education some 40+ years ago. But I understand that mathematics does two things: 1) Define new math, or 2) Derive new math. Newton had a physical model that he based his derivation of classical mechanics on. The gap in my understanding are the models behind the Lagrangians and Hamiltonians formulations of mechanics. They seem defined rather than derived and so appear arbitrary to me. For instance vectors have direction and magnitude and are easy to understand. But what does an "operator" have? Beats me. I would like to see some videos that fill in these gaps my education.

[@jeffpark1099]

Poisson bracket is wonderful bridge which can connect the clasiscal physics and quantum physics 😀

[@SelenGursoy]

I just started learning about QM and your videos open my mind in a very weird and beautiful way. Thank you so much!!!

[@darrellrees4371]

An absolutely crystal clear explanation of the subject. It did not remove the "weirdness" from QM as was not promised though!

[@schmetterling4477]

He can't promise something that he is not capable of.

[@alexanderbeliaev5244]

This channel can be a perfect place for Screen Cleaning Wipes adds :) I can not help myself, keep cleaning the screen while watching these wonderful videos.

[@tariq3erwa]

Today I learned that the canonical commutation relation can be derived from the definition of the cross product in terms of the clifford product of the position and momentum... It was mind blowing.

[@vivekpanchal3338]

This is really amazing, Watching your videos is really beneficial for students who wants to explore the theories, Really great work 👏👏🙏🏻

[@PhysicswithElliot]

Thanks Vivek!

[@amritawasthi7030]

#suggestion : Schrodinger equation. Explaining all that it contains without losing the mathematical essence. Thank you

[@topologo]

A beautiful introduction. I recommend to proceed showing as all of this follows from the Schwinger Quantum Action Principle 😉 Ask me for nice references.

[@darkrozen4110]

This is very cool. Are they are relationships with the lagrangian or other variables in the poisson bracket? for example Q1 = x, Q2 = L?

[@PhysicswithElliot]

Nothing interesting that comes to mind-you could look at Poisson brackets with the function p^2/2m - U, but I don’t know of any nice relations that result

[@thierrybm9101]

Very good video. I have a BSc in mathematical physics but end up doing quant finance... Ten years later, trying to re-read texts like Arnold's and Goldstein's Classical Mechanics is a daunting task but this kind of video makes it easier to regain intuition of the field. As a suggestion for the development of your channel, stick with relatively advanced stuff. I would definitely appreciate more videos on the geometric and symplectic interpretation of classical / quantum mechanics. Perhaps a video on the Dirac equation and/or particle physics would be cool as well.

[@PhysicswithElliot]

Thanks Thierry!

[@jngf100]

Really nice and clear account of link between poisson brackets and commutators - thanks for explaining this Elliot!

[@lepidoptera9337]

Don't mistake an ad-hoc quantization rule for real physics, though. It is, at best, theoretical hand-waiving. Neither the quantum to classical nor the classical to quantum transitions really happens that way.

[@Anubys1998]

love your work, im currently studying quantum / physical chemistry and your work helps me a lot to understand certaint topics. thanks for you videos, love from Slovakia

[@PhysicswithElliot]

Love to hear it, Adam!

[@sdsa007]

thanks, getting so much closer to understanding the Quantum world !

[@Eta_Carinae__]

Coming back to this video after learning a little more Hamiltonian mechanics, the Poisson bracket being 1 is the exact same as the condition for a coordinate transform to be canonical - that is, for the Jacobian of the transform M, and the canonical symplectic matrix J (as in, the one that spins everything 90 degrees anticlockwise), the Poisson bracket comes out of the condition that MJM^T = J. And this essentially comes from restricting your coordinate transforms to only the ones where Hamilton's equations of motion are satisfied (i.e. if you have some old coordinates q,p and some new coord.s Q,P, then \del H / \del Q = dP/dt and \del H / \del P = -dQ/dt). In short: the Poisson bracket is basically the condition for a change of coordinates that allows the same Hamiltonian to describe what's going on in the new phase space. EDIT: correcting one of the Hamiltonian EoMs.

[@katgirl3000]

This is Wonderful! I could have used this a week ago since our finals were just this week haha. You could also say "See this before you get to the end of e.g. Ch 13 of Taylor's Classical Mechanics!" :). I wish these were around when I got my undergrad degree in physics! Thank you! btw a video on Noether's Theorem in the Hamiltonian would be terrific!

[@PhysicswithElliot]

Thanks! Better late than never!

[@billy9021]

The bear really helped for my comprehension

[@physicsbhakt7571]

It's 4:37am in India Watching your video so early in the morning Nicely explained

[@PhysicswithElliot]

Good morning!

[@dennisbrown5313]

Really a good youtube on this subject - very important concepts; a very important topic that deserves more detail and examples in a follow up vid, please!

[@PhysicswithElliot]

Thanks Dennis!

[@kgblankinship]

Yes Elliot, definitely interested in Noether's theorem and its applications.

[@kashu7691]

these are some the best physics videos i’ve ever seen! please keep doing what you’re doing

[@PhysicswithElliot]

Thanks Kashu!

[@frogstud]

the possion bracket is more like a derivative because the jacobi identity is pretty much a product rule

[@DeepLyricist]

"You can't know the momentum and position of a particle at the same time." Why is Elliot always telling me what I can't do instead of what I can do?

[@PhysicswithElliot]

You can do anything you set your mind to! Except simultaneously measure the eigenvalues of two non-commuting observables. Or travel faster than c.

[@adventure.assistant]

In future videos, could you prevent the background from moving? It's way to fast if you are watching this video high. Otherwise is a super interesting video! I learned a bunch of relations I didn't know before.

[@jamesjackson5955]

Would love to see the Hamiltonian version of Noether's theorem

[@jarogniewborkowski5284]

Cool! Yes, please continue the subject and go towards Noether's theorem. Great job

[@PhysicswithElliot]

Thanks Jarogniew!

[@msergejev]

I agree with all the praises in the other comments, but I think it is understadted how excellent is your choice of topics. So far in the videos you made, you covered all the topics that I struggled to understand while trying to self-teach myself physics (mostly cause, in case of this concept and same goes for Lagrangian - they dont come of intutive concepts that map 1-1 to everyday physical quantities, I guess). Knowing to explain something in a clear manner is a skill indeed, but understanding what particular things other people might often not understand is a very important one as well.

[@PhysicswithElliot]

Thanks Amir! Very glad they've been helpful!

[@alexkong93]

Do more about quantum mechanics basics please, Elliott!

[@PhysicswithElliot]

Stay tuned AK!

[@nutashhacloves1230]

Wow, love at first sight with this channel. I discovered it because of Eigenchris. 😍 For the suggestion, can you please make more vids on String Theory. Thanks.

[@PhysicswithElliot]

Thanks Mishti! Glad you liked it!

[@meimeileigh8959]

h-bar is the reduced Planks constant. h/2π = h-bar h is Planks constant.

[@kianushmaleki]

Fantastic. Please make more videos like this one.

[@nicolascalandruccio]

Cristal clear, thanks! Please post the Hamiltonian version of Noether's theorem!

[@PhysicswithElliot]

Thanks Nicolas!

[@shivamgupta9967]

Why we assume the position and momentum are independent?

[@PhysicswithElliot]

At any moment in time you need to specify the both position and momentum of the particle (equivalently, the position and velocity) in order to say what it's doing

[@sachleensingh56]

Great explanation as always! Can you come up with a simiar video on Maxwell's Thermodynamic Relations or Quantum Stat or Ensemble Theory of Macroscopic systems?

[@PhysicswithElliot]

Thanks Sachleen! I will think about your suggestions!

[@robertcantwell9569]

Once again thank you for a lucid and engaging presentation .

[@PhysicswithElliot]

Thanks Robert!

[@yairraz6067]

Hi Elliot your videos are amazing and it would be really fantastic if you could do some videos on quantum filed theory.

[@PhysicswithElliot]

Thanks Yair!

[@General12th]

I took AP Physics C during my last year of high school, but I don't remember learning anything about Lagrangian or Hamiltonian mechanics. Then I took undergraduate modern physics in my first year of college where all of this was assumed background and we could jump into the meat of the course right away. Maybe I just missed something. Either way, I'm glad I can start to actually learn this stuff and it's not a condensed, impatient mess.

[@PhysicswithElliot]

Oh yes it’s certainly not covered in high school physics, or even college freshman physics usually. So it’s common to try to cram a little in to the beginning of a quantum mechanics course, but that doesn’t necessarily quite do it!

[@norbertprebeck2024]

Thank you very much! I highly appreciate your videos. Please, show more content of QFT.

[@spiguy]

Another video to add to your banger video streak Just one question: how do you go from the classical {x ,p}=1 to the homologuous Qm 1/(ih_bar)[x_hat , p_hat] ? Maybe I lost focus somewhere because I only couldn't grasp that

[@spiguy]

Oh, lemme check the notes, I almost forgot about those! Maybe I can start to like homework now lol Your lessons are great reminders to me, but they also expand a bit on stuff I had already seen! Keep it goin

[@PhysicswithElliot]

Thanks Arnaud! Oh I certainly didn’t explain why it works that way in going from classical to quantum mechanics, I only stated the rule without justification

[@nicolascalandruccio]

Same question. I don't see the link between classical {x,p} and QM [x_hat,p_hat]. For instance, why there's a 1/(i*h_bar) factor? Maybe, I have to check the notes and the previous videos.

[@zray2937]

You can't give a proof or a demonstration of that transition, because QM is not contained in CM. Only a reasonable justification can be given. See chap IV of Dirac's principles of QM.

[@AlbinoJedi]

This was so well explained that I subscribed. I'll have to check out some more of your videos.

[@ninjakingcola]

Please more on the Hamiltonian Noether's Theorem

[@andreantoine8005]

Def would have enjoyed this in undergrad

[@Dismythed]

It makes perfect sense if, and only if, you take these equations to be representing two smaller particles (i^2) spinning about an axis (ħ^2). That's why it only works for objects with spin 1. Objects with spin 1/2 end up looking fuzzy because they are 3 particles which are spinning about a double axis (possibly, i^2 x i' x ħ^2 x ħ' where the special operator has yet to be defined at the moment; however, much of its mass gets transformed into electromagnetic voltage. E=m^2c^2=hf). This is because photons are made of two smaller particles creating the photoelectric effect, and when we add a third particle, it registers as mass, instead of electromagnetism. This is because the smaller particles making up the photon are the mass carriers, but they get transformed into electromagnetism by their spin. Adding a third particle allows it to retain its original mass. The lesser particle has spin 0 (Higgs modified) because it is indivisible. The 3-body system can be expressed in one of 3 ways: a spinning triangle of particles (quarks) whose attraction creates a tether (positive remainder) to which other quark trangles (nucleons) and electrons are attracted, two spinning particles periodically trading places (electron), or a cone shape in which two of the particles spin at the back while one remains in the lead (neutrinos). However, the number of indivisible particles in each larger particle of each configuration is varied. There could be tens, hundreds or thousands of photons making up any particle. What binds the two indivisible particles to make a photon is their need to eliminate the space between them (Nature abhors a vacuum). They prefer to travel at instantaneous velocity (their rest state), but the existence of other particles creates gravity, causing each to become a monopole that causes them to bind with a partner. But because they need to move forward but cannot separate, they spin about each other at an angle causing parallax. Because they can never meet, they generate a counterforce to each other, destabilizing their gravitational monopoles into a dipole electromagnetism, no longer registering as mass. But introduce a third particle and its mass registers. The total electromagnetism and mass tell us how many indivisible particles there are in the structure. The mass tells us the number of third indivisible particles and the electromagnetism tells us the number of photons (pairs of indivisible particles). I'm still working on the math, but that's the latest model.

[@JosephChan4701]

Beautiful video! What software did you use to make it?

[@PhysicswithElliot]

Thanks Joseph! This one I made mostly in Keynote.

[@yexela]

It would be nice to have a relativistic version of this video.

[@khanhphamquang1510]

[x,p] should be equal to 0 at classical limit! Since at the classical limit, the Planck constant \hbar goes to 0!

[@stevenicoletti3498]

Yes please do explain Noethers Theorem and work it out with Hamiltonian formalism.

[@PhysicswithElliot]

Already posted!

[@mootal2812]

Elliot, This video is excellent! Do you a Math book list to prepare for studying of Quantum Mechanic?

[@schmetterling4477]

Before you study quantum mechanics, take an introductory course in atomic physics. It will reduce your stress levels greatly.

[@afakcay]

Released at the perfect time! Wonderful explanation, kudos to you Elliot, thank you!

[@afakcay]

Also could you do a video on Lagrangian and Hamiltonian dynamics. That topic also looks very confusing but after watching this video, I discovered what complicates topics are the lack of emphasis given to the foundation! Thanks again

[@afakcay]

No way!! you already have it! :) Sir, you are something else. Man like Elliot, legend!

[@PhysicswithElliot]

Glad it helped Abdullah!

[@kvathishpranav4112]

8:14 we do need, plz go ahead

[@Mysoi123]

Thank you! very helpful on such an abstract topic.

[@PhysicswithElliot]

Thanks Aihara!

[@SohailSiadat]

Please explain more about Noether’s theorem and its Hamiltonian versus Lagrangian versions

[@PhysicswithElliot]

Made two videos about Noether's theorem, check them out!

[@speeshers]

This video was amazing, thank you! Would love more higher level content from you :)

[@PhysicswithElliot]

Thanks Abhay!

[@cesarjom]

This was awesome little insight!

[@PhysicswithElliot]

Glad it was helpful Cesar!

[@_kantor_]

Extremely useful as always! Can you do some difficult examples? I usually find surface level explanation (as good as they may be), but I NEED deeper level explanation to help my understanding. Great content and thank you! Love from Tel Aviv

[@PhysicswithElliot]

Thanks Dan!

[@jacobvandijk6525]

Triple-A video. Thanks! Is "diagonalization" an option for a new video?

[@PhysicswithElliot]

Thanks Jacob! And maybe!

[@ricomajestic]

Would love to see a video of Von Neumann's No hidden variables theorem since it is not covered in any undergraduate QM book. The theorem was very controversial and led to John Bell's theorem. Practically no videos on youtube about it.

[@officiallyaninja]

please make a video on Hamiltons version of noethers theorem. it sounds awesome

[@farooq8897]

Can I know what tools you are using to create this content?

[@pawanmarahatta5749]

In Rutherford gold foil experiment, according to classical mechanics, why accelerating electron should lose electron?

[@mandaglodon]

I lovee this!! Thanks for always making us learn something new clearly!

[@PhysicswithElliot]

Thanks Aman!

[@TariqKhan-bh9pm]

Sir, could you explain the role of Planck constant in Heisenberg uncertainty principle.

[@TesssyTosco]

quantum mechanics is not weird but it is absurd and interesting, just like you Mr. Elliot

[@paulbizard3493]

How nicely put. 👍 Thanks Elliot.

[@sweetpotatoambassador]

Really great video! I would love to see a video on the Hamiltonian version of Noether's Theorem :)

[@PhysicswithElliot]

Thanks Nick!

[@physira7551]

can you do QM video series which covers the basics ? i am a math student but want to know more about QM

[@PhysicswithElliot]

I certainly hope to do more QM videos in time!

[@sahhaf1234]

yea pls.. do the hamiltonian version of noether also..

[@kashifahmad602]

Sir Schneider is great

[@NikolayCherednychenko]

Definitely explain hamnotheorem

[@DargiShameer]

Great explanation 😍😍😍😍

[@Mysoi123]

Hi Elliot. Do you have any suggestions about what type of physics should I learn and what playlists should I watch before starting QM? I have an Issue with symbols and notations in QM. Thanks a lot!

[@WestOfEarth]

So that's all there is to phase space?? I mean, it's probably a bit more complicated, but I never had a solid grounding in what phase space actually meant. Thanks!

[@PhysicswithElliot]

Well this is the simplest example!

[@WestOfEarth]

@@PhysicswithElliot But still...when I heard lecturers or grad dissertations use the term 'phase space' I had no idea what it was. But now I have an inclining. Thanks.

[@hichemzerdi1580]

what programm you're using to create this kind of vidoes

[@jackflash8756]

Why is partial derivative of momentum with respect to x = zero (and vice versa)? Momentum depends on velocity , which also depends on change in position x with respect to time.

[@khaloscar]

From calculus we know that the order in which we take different partial derivatives of a function does not matter. These operations commute. So imagine taking d/dx first and then d/dt. This gives dx/dx = 1 and d1/dt=0. This, is equal to d/dx dx/dt, so its zero.

[@jackflash8756]

@@khaloscar - Many thanks.

[@jackflash8756]

Many thanks

[@dariazafote5522]

Gold. Awesome video, keep it up! Thank you so much! Subscribed.

[@PhysicswithElliot]

Thanks Daria!

[@CAL-1442]

please cover Hamiltonian Noethr Thm. in another video. Thanks.

[@sitaramar13]

If we toss a coin also , before experiment, we have only a probability. After experiment , we have a definite result. What's difference between this and behaviour of electron ? Why do we call collapse of wave function ?

[@xjuhox]

But _why_ are position and momentum connected in quantum mechanics? What is the physical reason behind it? Given the backround potential, position and momentum determine the energy state of the system of a particle. That is, at the micro level the energy is somehow a fuzzy concept and does not allow complete information. Interactions give information and information causes fluctuations that in turn cause interactions with the enviroment. We live in a strange, wavy and nonlocally interconnected Universe...

[@krzysztofciuba271]

You(@i assume plenty others) an example of the failure of textbooks to properly explain the foundation. QM is a statistical theory and not that of a (individual) particle (like photon, electron, etc)! Experiments give the results of the reaction of a measuring device with such a bunch of "quanta" of some field,for example, electromagnetic field: the double-slit experiment is a perfect example of it (one deals with a wave-field (of quanta) reacting with the screen. Textbooks example of the so-called wave nature of a rigid macro-object (lie a ball) is a total educational BS because QM does not deal with both an individual "object" and this "particle-object" as a macro-rigid object (the model of field is not that of a rigid object,and consequently the relations regarding the position, time,etc: energy, momentum,..).If any textbook starts to write about a "particle" it means the author does not understand QM at all; consequently this opinion about the "weirdness"; for the wave (wave/field does not move), the momentum does not depend on the position (of the point of quanta that is not moving but only oscillating); here, the thought model of Heisenberg is fooling himself and readers: it depicts an electron as a "point-particle" that moves and not as a point of quant-electro field that does not move (field does not move,it is standing) but his equation, deterministic as any statistical one rightly predicts the outcome of the experiments

[@xjuhox]

@@krzysztofciuba271 Do you know why position and momentum *distributions* are connected?

[@krzysztofciuba271]

@@xjuhox for electromgt. field:c(angular speed)=Energy/momentum then analogically for any so-called"matter" wave the same relation but one does not have a monochromatic wave but only a wave packet.; the momentum is not the function of position ( a wave is not moving) - for any wave and ...in the Lagrangian models.

[@n_fieldgaming]

Thank you so much sir for this video ❤✨

[@nerdphysics6402]

Amazing video thank you ❤