Quantum Physics Becomes Intuitive with this Theorem | Ehrenfest's Theorem EXPLAINED

[@nyahanderton4912]

I do a physics degree and these videos are making it so much easier for me, the lecturers tend to over complicate everything

[@hafsashabbir7842]

You are my favourite. Physics is not fiddly and subtle. Just need a best teacher to explain it and u are:)

[@FD-rt3rv]

this video evokes two strong feelings: the first is that i love you and your videos, the second is that I deeply detest my smart-cookie-expensive-profs who cannot do their job properly and explain such concepts nearly 1% as clear as you do

[@romishcraft]

Thank you so much Parth. I was really tired of watching philosophical or theoretical physics. I thought there is no KZbin channel who gets into the equation, but I am glad that I found your channel now. People like you makes KZbin an amazing place. Thanks again.

[@ParthGChannel]

Hi friends! The first 1000 people who click the link will get 2 free months of Skillshare Premium: skl.sh/parthg0820

[@arhenresleff4748]

Hey, my name is Arhen and Im striving to major in quantum physics/mechanics and for a PhD in Astrophysics and astronomy. I've heard of ehrenfest theorem before however this was an excellent explanation! I found it very helpful and ive been working through your other videos as well, can't wait for the one on entropy! Thanks Parth 😀

[@zigazagateam]

It seems as Mr. Feynman one time said that "If you can't teach something to a 6-year-old, that means you don't really understand it". Obviously I am not 6-yo, and although I am en engineer in computer science, I am just a newborn in Quantum Physics. However, while listening your explanations I feel like a 6-yo kid understanding what you are explaining, which means that you have a brilliant mind and that you are an amazing teacher. Thanks so much. Physics needs more people like you.

[@markusantonious8192]

As a teacher (emeritus) myself....I can tell you - though I rather doubt you need convincing - that Parth is an absolutely superb communicator and teacher.

[@tobydunbar1153]

You are an EXCELLENT TEACHER!!! Thank you for all the amazing videos!!! Your long hair looks lovely, by the way!!!

[@ParthGChannel]

Thanks so much Toby :) I appreciate the kind words

[@lewisleslie2821]

Ohhhhhh that makes so much sense!! This was a good refresher on commutation too! Looking forward to that entropy video :))

[@SMc-1235]

So this is the use of Ehrenfest's theorem. Thanks for the lucid explanation ❤️.

[@vineethvenugopal8613]

Thank you so much Parth. It was such a simple and beautiful explanation about operators , commutators and finally about the essence of ehrenfrest theroem.

[@aritrakundu1464]

I am a first year UG student at IIT Kgp and here I am studying Quantum mechanics for the first time, just 3 hours before the test....Pray for me

[@anjalibhattacharyya4940]

Sir isn't h bar = h/2π(where h is Planck's const.) ..... excellent explanation btw and please make a video on special theory of relativity.

[@ParthGChannel]

You're totally right, that's my mistake! Good spot :)

[@pranjaltiwari1663]

Reduced Plank Constant

[@robertschlesinger1342]

Very interesting, informative and worthwhile video. Parth, you are raising the consciousness of the world. Bravo!

[@juniorcyans2988]

Thank you so much for showing those lines on the screen. They were what I was looking for!

[@kandasamymarimuthu6640]

Excellent video on quantum operator. I actually started pick on quantum mech. During covid lock down in Malaysia starting march 18,2020 just to keep my mind active and so interesting the way you capture the topic and your English to easy to catch phonetically due to Indian flair.thnx

[@kunalverma6940]

Apart from the awesome explanation of Ehrenfest theorem, you gave an equally amazing statistics lesson for the difference in averages and most probable values, lmao. Also, could you delve deeper into the topic about why Quantum Mechanics inherently uses complex numbers and complex functions?

[@xjuhox]

Complex numbers are two dimensional numbers that can incorporate real variables X and P. The crusial Fourier transformation is a complex transformation between two basis variables, i.e. X and P. And, of course, the Fourier transformation is equivalent with the Heisenberg's commutation relation [X,P] = ih that is the key to the matrix mechanics.

[@marcusrosales3344]

Given Schrodinger's equation this has to be the case! The free particle is just a diffusion equation with a imaginary diffusion constant. It's solution is quite intuitive: a plane wave with a phase relation kx-Et. The factor of i does something special: it makes so a single time derivative can support oscillatory solutions. It makes the plane wave solution possible for a free particle. In any case imaginary numbers are for real! Aerospace engineering has complex drag coefficients for instance.

[@nandanshettigar873]

Excited for the entropy video

[@kartikmessner2868]

Beauttiful.. : ) made the picture much more clear compared to when I read the text first.👍🏻👍🏻

[@nileshkulkarni6196]

Your videos are awesome 👏 .......love from 🇮🇳....

[@xjuhox]

You could mention that the Schrödinger equation can be derived from the Ehrenfest's Theorem if we assume the "fundamental transformation" between position and momentum.

[@qubex]

10:32 I scanned through the commentator algebra and saw the end result so I said to myself “heh, momentum’s expected value divided by mass, that’s basically velocity, so when observing location your expectations follow the expected velocity, yeah that makes sense”.

[@schmetterling4477]

I would suggest that you look up the physical requirements for velocity measurements and then compare with what can and can not be done in quantum mechanics.

[@joumanic]

Hey! My classmates and I really love your videos!! they saved us so much time and effort. Would you be able to make a video about angular momentum in spherical harmonics and perhaps also the zeeman effect ?

[@ronaktiwari7041]

How could I have missed subscribing a wonderful wonderful physics Channel like this....!

[@eldestisland4520]

Thanks for writing out all the math at 10:30 🙏

[@quahntasy]

Very informative video. Thanks for this. Loved the way you connected quantum and classical mechanics

[@ParthGChannel]

Thanks so much :)

[@nileshkulkarni6196]

Quahntasy-Animating Universe I have seen you before in some other comment section (maybe Kurzgesagt or Teded ? ).....and you are from IIT Kanpur Can u give me some tips for studying to score more in JEE I love how a lot of youths from India 🇮🇳 are following some gr8 channels like Parth G , Kurzgesagt , Ted-ed ,etc. And I see you too animate some good educational videos...... keep it up👍

[@EarlWallaceNYC]

very insightful. Thanks

[@traruhsynred3475]

I don't get why you say is equivalent to doing a measurement. x|psi> doe not result in a new wave function confined to a single point. That would be impossible anyway as it would take infinite momenta to specify. Indeed all you get is wave-function multiplied by x and that is not even a normalized wave function nor does it pick out a particular value. which involves an integral of x does calculate 'expected' value, but again does not pick out any particular value. Doing a measurement always involves a n interaction with something and can't be done by applying an operator to single particle wave function. Typically it involves some kind of irreversible event such as a charged track ionizing an atom that seeds the formulation of a bubble. The precision of the measurement rarely (if ever) probes anything near the Heisenberg limit.

[@rijuwanahaque8054]

Just found this channel. Now addicted to it.💙 I am also a Physics Student working on Material Physics !!! But interested in QM and CM🙏🇮🇳

[@lakshthaker6379]

best videos made by you. fav youtuber

[@ParthGChannel]

Thank you so much :D

[@gowtham5168]

Love u brother ... u make it elegant and importantly u make us appreciate the concepts

[@ankitaacharjee3283]

Very effective explanation .thank you making physics interesting

[@selin4393]

saved my life, thank you

[@asukayanami7159]

best explanation video ever watched! thanks a lot

[@voidisyinyangvoidisyinyang885]

Basil J. Hiley has proven that to have conservation of energy of the wave function there has to be a quantum potential that is nonlocal and noncommutative.

[@satyanarayanajoshi3239]

Hi i am getting more curious in physics by watching your videos Thank you very much 😊😊

[@ParthGChannel]

Thanks so much for watching!

[@satyanarayanajoshi3239]

@@ParthGChannel Thanks for reply 🙂🙂🙂🙂

[@ehosseinnn]

This is excellent but I think you have a big mistake that could confuse many: The vertical axis is NOT probability but pdf instead(area under the curve is probability..)

[@user-vg7zv5us5r]

7:37 There is not particular time unit since dt is infinitesimally small quantity. Check out Leibniz's Law of Continuity.

[@abdulrahmanalhamali1707]

Great content, thanks!

[@nabhoneelchatterjee2692]

very simple and clear explanation sir..💙

[@pritivarshney2128]

Excellent video! Now I really understood the relation between Quantum Mechanics and Classical Mechanics. Can you do a General Relativity video Please?

[@ParthGChannel]

Thanks! Yeah I want to make some GR videos for sure :)

[@sarniva]

Excellent video ❤️❤️

[@ParthGChannel]

Thank you so much!

[@sarniva]

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[@tzaidi2349]

Love this material and presentation style. Subscribed!

[@sdsa007]

Thanks very challenging topic!

[@ahmedsaeed7158]

Keep rising up ♥️

[@harshbhogal4439]

loved every single second

[@ParthGChannel]

Thanks so much Harsh :)

[@divyadeepsingh9062]

Hey Parth are you planning to make a video on decoherence ?? That could be a topic

[@MosheTarko]

Could you please do a few examples (with numbers) after you explain the formulas?

[@ffhashimi]

Yes it would be great.

[@joeyrufo]

I feel like it has to be important what you have to go to a pair of electrons to get them into an "entangled space"!

[@ec6093]

This is so cool!!! You did make the process look simpler, thanks!

[@ratnabesra8959]

Great explanation

[@sreedevipv8749]

Sir...can you can make a video on quantum engineering....love your videos!!!

[@lakshthaker6379]

Sir please make a video on Copenhagen interpretation

[@tadeletekeba13]

Thank you so much for beautiful explanation

[@TheHumanHades]

Sir, if expectation value of rate of change of a operator is always zero then why is it even there in the equation. Is there a case when it is not zero? Amazing video though 😀

[@xepho8205]

The X operator is time independent. There might be cases though in which an operator A does depend on time so the last term must be included in the general formulation ... The Hamiltonian for instance (the H operator) may be time dependent when there is interaction between light and matter, then the electric and magnetic fields of light contribute a time-dependent part to the potential energy experienced by the atom ...

[@abhishekrai1204]

Sir plz make video of classical mechincs imotant topics as lagrangian mechincs phycial mean etc

[@ParthGChannel]

I definitely want to do that :)

[@sandeepgodiyal5686]

Hi Parth, I have one question... In the expression of Ehrenfest Theorem, the third term represents the expectation of rate of change of operator. As you were telling the measment changes with time but the process of making measument (operator) doesn't change with time, so essentially this term becomes zero. If it is zero only, then why this term is included in Ehrenfest Theorem?

[@xepho8205]

The X operator is time independent. But there might be cases in which an operator A does depend on time so the last term must be included in the general formulation ...

[@DanielL143]

Excellent.

[@georgearrington5766]

Another good one!

[@abhinavsrivastava8457]

Hawking radiation does also link classical mechanics and quantum mechanics

[@ParthGChannel]

Very true, it uses principles from both relativity and QM

[@spyrex3988]

Yoooo the new hairstyle is sick

[@ffhashimi]

Great!; I suggest and hopeyou talk about a real example of simple measurement system and it's calculation; in other world a simple real example of what physicists do when they make a measurement and calculate its result; this would make things sink in; thanks

[@vijaysinghchauhan7079]

At 4:05 there are no resources for mean and expectation values in the description.

[@ocean7371]

Wow 64k , following you since 1k

[@ParthGChannel]

Thank you so much for your continued support :D

[@user-gl2eq2ly4g]

Love it ...... Thank you

[@sergiolucas38]

very good video, thanks :)

[@muhammadjawadkhan6407]

Sir in quantum physics and classical physics there is difference of h bar ?

[@user-vg7zv5us5r]

11:20 Don't you mean that Ehrenfest's theorem nullifies Heisenberg's uncertainty principle since we can now determine position (coordinate) and the momentum (impulse) even though approximately?

[@voidisyinyangvoidisyinyang885]

no because of the actual quantum measurement problem being noncommutative - he explained that in part one. He just didn't say it was noncommutative even though it is! thanks

[@vishank7]

Loved this mini series Parth, keep up the good work! I have a little doubt. I see operators as a mathematical equivalent to functions, like x(psi) and f(psi), which ends up being a normal scalar valued function "f" giving us the position of our particle. So, it is kinda weird to think about commutators defined like xH-Hx. It is like defining a quantity f•g-g•f which has no meaning.🤷‍♂️

[@xjuhox]

Those terms are like matrices that are linear transformations that, in general, do not commute, i.e. AB is not BA.

[@vishank7]

@@xjuhox That actually clears things up. Thank you!😄

[@angelmendez-rivera351]

Actually, if you study functional analysis, you will realize that the expression f•g - g•f makes perfect and is well-defined. Functions are mathematical objects just like any other, so we can treat them like mathematical objects and define operations as we like. Things in mathematics have meaning as long as mathematicians want it to have meaning, because meaning is not an inherent property of objects. So in fact, it is not even necessary for you to think of H or x as matrices - in some contexts, this interpretation of operators is not even possible, which is why wave mechanics ends up forming part of the basis for higher level quantum theory.

[@unrealreality5419]

Amazing teaching! You have a rare talent!

[@jaybhambure5969]

Nice video! A tiny but important correction at 11:30-11:40 all the probability graphs are incorrect, at the nodes. Your graphs are non-differentiable at the nodes. Make sure that all graphs are differentiable at all points in order to use Ehrenfest theorem. A counter example is the bound state of a 1 dimensional Dirac delta potential, whose solution does not follow Ehrenfest theorem, since the solution is not differentiable at the location of Dirac delta. Hence we use an alternative interpretation for the same. The interpretation being that the delta potential is only a quantum phenomenon and has no classical analogue.

[@angelmendez-rivera351]

This correction isn't actually very important, since this video isn't meant to be a rigorous proof or explanation of Ehrenfest's theorem. Instead, it's meant to provide an intuitive guide for understanding the theorem with a level of knowledge that a high schooler would have. And you can trust me when I say most high schoolers won't've any idea of what "differentiability" means. It's entirely outside the scope of the video, and such tiny details aren't relevant to the intuitive explanation, which is something that was literally clarified in the previous video on the topic. You can't judge the execution of a video by the standards of what it wasn't meant to do. That's logically fallacious.

[@mahboobhossain3301]

The time dependent Schrodinger's eqn. doesn't involve probability then how probability entered into QM when all means are too deterministic???🤔🤔

[@Jehannum2000]

Your English is not very clear. It's hard to understand what you are asking.

[@abhasoodan7982]

i have a question, in the last term of RHS of this theorem, why do we need to write it down if its going to be zero? are there cases where its not 0?

[@tamiltamilan2208]

Hello sir your videos are superb and good and however I think that you will be really satisfied if you refer previous year NEET and AIIMS question papers. Well the are the medical entrance exams of India and there are myths that are spreading that the physics questions in these exams are extremely tough. Well so feel free to check it out and make a special video reviewing them. Please Note: It's just my recommendation

[@tamiltamilan2208]

Sir if you do that it would be helpful. Pls sir

[@blueTwl]

can anyone tell me what is this program that Parth is using? I think it's a really nice way to present the mathematics and would like to use it

[@carlthorellstein53]

Wait hollup; if we can do the exact same experiment twice, at different times, and get different results, does that not mean that one of the conservation laws in Noether's theorem is violated? Or rather, that one of the conservation laws do not hold when looking at quantum systems? Or is that because I'm tied to the idea of particles having definite positions always, rather than viewing them as wave functions first and foremost?

[@schmetterling4477]

Neither. All conserved quantities in quantum mechanics are conserved in every repetition of the experiment. The actual problem you are running into is that the theoretical description is not self-consistent. The potential in the Schroedinger equation acts on "the particle" but the particle does not act back on the source of the potential, hence you are automatically violating conservation in the math, even if the physical systems are not. That's just one of the reasons why one should not take the Schroedinger equation too seriously. It's a toy quantization procedure that teaches very little about the actual structure of the world.

[@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 ?

[@schmetterling4477]

If you are a rational physicist, then you will not use the "collapse of the wave function" terminology. A wave function is not a physical property of the individual system. It is a the description of the free dynamic of the quantum mechanical ensemble (i.e. of infinite repetitions of the same experiment). Unfortunately there is no physical meaning in that ensemble description all by itself. The physical meaning only exists if we also describe the preparation (emission) and measurement (absorption) conditions of the system. Only if all three elements (how we put energy into the system, how the system evolves and how we take the energy back out, again) are completely specified, can we make an actual physical prediction.

[@sitaramar13]

@@schmetterling4477 thanks sir

[@sudhanshusharma5497]

Man...you are very cool!!!

[@sonugeorgealex]

Detailed explanation of those 'p' substitution would have been nice or atleast should have mentioned the steps 😉

[@daanvanijcken4288]

Shouldn't it be rather than ?

[@Jehannum2000]

No, you don't need the asterisk in Dirac notation. The bra is already defined as the complex conjugate of the ket, and their labels are just labels.

[@saradhicheruvu7585]

Just curious. Since expectation value is loosely tied to average value, for a given distribution why would an expectation value change with time?

[@ParthGChannel]

Great question! Because the distribution itself evolves with time. For example, the Schrodinger equation determines how the wave function changes over time, and this means the probability distribution of the system changes with time too. Therefore, the expectation value does the same.

[@saradhicheruvu7585]

@@ParthGChannel Thank you very much. It is very clear now. I learnt a lot from your videos than reading books on QM. You made a complex subject easy to understand. Now I am really enjoying QM. Wish I had a teacher like you when I was in school.

[@xjuhox]

The expectations values evolve in time (the Schrödinger equation) and for every fixed time, the wave function Psi(x,t) gives an expectation value for any physical operator O as an integral .

[@rc5989]

Is this related to momentum and velocity being treated separately and equally by Hamiltonian operators, instead of Newtonian mechanics which treats momentum as derived by position and velocity?

[@xjuhox]

In QM the momentum P is an operator that takes the X derivative. That is, in QM the momentum and position are indeed related.

[@HeroSanjA]

Hey how do you draw in your videos? :)

[@muhammadjawadkhan6407]

Why we only study angular momentum in q.mechanics

[@schmetterling4477]

We don't. We study energy and momentum and charges and their spectra and scattering amplitudes. Angular momentum simply happens to be one of the quantized quantities.

[@Dismythed]

I'm curious why the theory uses absolute time (dee-tee) instead of relative time (dee-tau) since we're dealing with objects in motion? (Or maybe even plugging in the dilation equation?) When scaled up in either velocity or length, there will be time dilation and length contraction, won't there? Or does that come later down the line? Solution found in my comment below.

[@schmetterling4477]

Non-relativistic quantum mechanics doesn't care about the difference. It doesn't have to. It can't describe systems of multiple particles correctly to begin with and the multiple observer problem can't even occur because each measurement in quantum mechanics is a monad (it can only occur once). Relativistic quantum field theory, on the other hand, is Lorentz invariant by design.

[@Dismythed]

@@schmetterling4477 I believe what you're referring to in regard to Lorentz invariance is Loop Quantum Gravity. This, on the other hand, is Ehrenenfest Theorem. I just read the Wiki page on it and now I understand that it uses absolute time because it is relying on classical mechanics for the operations and letting Poisson's bracket and the Hamiltonian do all the heavy lifting. The expectation values, as Parth explained, which are the purpose of the equation, allow the link between quantum mechanics and classical mechanics. Basically, it's a mathematical lingual translation between Newton and Hamilton. At 8:54, I missed that he explained that "the process of measuring itself does not change with time." In other words, the measurer and the object measured do not have significant changes in position with relation to each other so that they do not significantly impact the result. I feel kind of foolish now for having missed that and the direct reference to classical mechanics.

[@schmetterling4477]

@@Dismythed I don't know how you came to these strange beliefs. LQG is nothing more than a hypothesis at this point. QFT is well established theory. Quantum mechanical measurement is irreversible energy transfer, hence it relies on energy, which does not exist without a classical time concept.

[@Dismythed]

@@schmetterling4477 Please don't paint me as a nutjob. Not everyone has the same level of knowledge. My bad on the Lorentz invariance. I haven't gotten that far into physics yet and looked up an article that was a specific application of Lorentz "invariance" rather than its general application. But the rest of what I said is accurate. I now understand that Lorentz symmetry is the source of the idea that physics is the same for all observers. I'm just not familiar with the math yet, though I absolutely believe the principle. I just never made the connection to its name. The "invariance" (correctly "covariance") is the claim that the symmetry is hard-baked into the backround of the universe (QFT), not just natural to the math. If I understand that correctly, then I'm not sure how relativistic QFT answers my original question. I kind of feel like your original reply was to the left of what I was originally asking for. I was asking why, not asking for an opinion of what view is correct. I'm not being aggressive, just honest. If you want someone to learn, you need to give them the facts and leave it up to them to develop their own opinions.

[@schmetterling4477]

@@Dismythed I gave you the answer. Non-relativistic quantum mechanics is a toy theory that doesn't care about these things. It's not correct and it can't be made correct with "small" changes. The correct theory is quantum field theory, but that correctness comes at an incredible level of mathematical complexity. I can't change that for you. The reason why we don't get people started on QFT is simple: it is too hard for all but the most gifted students. I am an experimental high energy physicist but I can't do a single line of QFT calculations myself. I can measure what the theory predicts, but I can't use it myself. I have to rely on the theoretical guys who can to do it for me.

[@rajaradi802]

Parth what does it mean for something raised to the power e or e raised to power of ih or something

[@xjuhox]

Just check the power series representation, baby. If the shit converges (in a norm) and is unique, then it makes mathematical sense.

[@rajaradi802]

@@xjuhox Iam not a baby

[@sumapanattu117]

dude i wish you could reply to this comment i always have the anxiety that i will not understand the concept before studying the concept itself the really problem i have is that i always think that i will never reach an expert level understanding of physics i actually have reasonable intelligence but still i have anxiety can you help me with this

[@reemibrahim4847]

Hey💜

[@ParthGChannel]

Hi :D

[@tadeletekeba13]

Thank you so much Parth G (Tadele __ Ethiopia)

[@br3nto]

Everyone keeps saying that quantum mechanics is unintuitive and difficult compared to classical mechanics... the more I learn the less this seems true. The problem is that we aren’t taught classical models first and get all these false models first, then we learn the quantum models. Schools should just skip the classical stuff and teach the quantum stuff.

[@schmetterling4477]

Classical models aren't false. They simply don't tell you about the structure of matter. They only tell you how large chunks of matter move.

[@johnpaulbounce3708]

High school level math? Parallel universe is real. Lol Nice vid.

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👍🏻👍🏻👍🏻

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Kingg

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[@ParthGChannel]

Hi :D

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Om Vedant Chimmalgi hi

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Hi

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Hiya :D

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[@ParthGChannel]

Thanks for watching :D