Position and Momentum from Wavefunctions | Quantum Mechanics

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In this video, I define the expectation value of position for a wavefunction psi and use that to derive the expectation value of momentum as well as the expressions for the position and momentum operator. I then show that in general, any Classical Mechanics quantity can be determined from the wavefunction using a combination of the position and/or momentum operators.
There's quite a bit of math involved, so if you have any questions, let me know in the comments! Stay tuned for the next video (coming soon!) in which I will use the expressions for the momentum and position operators to derive the Heisenberg Uncertainty Principle.
Prerequisites: All the previous videos in both of these playlists (Playlist 1: • Quantum Mechanics , Playlist 2: • Quantum Mechanics: Mat... )
2nd Postulate Video: • Commutators and Eigenv...
Previous Video: • Introduction to Quantu...
Lecture Notes: drive.google.c...
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Twitter: / facultyofkhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
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Опубликовано:

2 окт 2024

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Комментарии : 56

@_DD_15 6 лет назад

Mate please hurry up with these videos, they are absolutely amazing!! Much appreciated, somehow the way you explain is the same way I learn things. Because I grasp everything in 1second from your lessons. Thanks a lot! I like the way you teach stuff, the detailed mathematical description. Simply perfect!

@medtabernoust3869 3 года назад

u are the best i swear u are the kind of teacher that i like, u give since to everything thank u so so so so much for those amazing video

@munish6957 4 года назад

Your videos are amazing... can you plz elaborate or make a video on 'how you create these videos', i mean what all hardware n software needed...

@bikashbora5801 6 лет назад

Please make an video on Schrödinger and Heisenberg interaction pictures

@fosheimdet 5 лет назад

Why does the total derivative become a partial derivative when you move it inside the integral at 3:57?

@ztac_dex 4 года назад

because psi is in terms of x and t , not just x (explanation from Griffith's QM)

@domzi2 3 года назад

its called Leibniz integral rule, read more about it if you are interested why exactly

@julianandresflorezsolano1745 3 года назад

This is 10 times better than the lectures my professor gives

@arhaankhan6714 2 года назад

I do not get it. The convergence of the improper integral does not imply the convergence of the integrated function...

@dailydoorsteprangoli9179 2 года назад

How u create these videos? Hardware n software ...pls suggest

@ostensiblyquerulous 6 лет назад

Could you discuss the collapsing of the probability distribution to a delta function in a future video?

@FacultyofKhan 6 лет назад

I discussed it briefly here (at about 5:03): ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-kUm4q0UIpio.html&l=

@Hevander75 6 лет назад

thank you for making these videos

@alphabetgpt4 3 года назад

Ini bukannya sebelah mana?👍

@giladreti 6 лет назад

I do not get it. The convergence of the improper integral does not imply the convergence of the integrated function...

@FacultyofKhan 6 лет назад

You're right, but pretty much every function that you'll see in Physics obeys that rule. I mentioned this in the description of the Schrodinger equation video. The only functions that have a convergent improper integral but themselves don't converge are exotic mathematical functions; we don't have to worry about those for a Physics course. Hope that helps!

@giladreti 6 лет назад

Okay, thanks!

@giuseppeguap7250 5 лет назад

Bless your youtube soul

@jacobvandijk6525 4 года назад

From 3:37 until 8:31 only hard-core math; no physics to be found there.

@dracowolfe305 4 года назад

Felt like being underwater for 5 minutes

@atwellbill 2 года назад

At 8:41 in this video, you write the expectation value of momentum as the product of the mass and the (postulated) expectation value of velocity. But is this non-relativistic term for momentum applicable here? What about atoms where the electrons are moving such that expectation value of velocity

@novocaine212 4 года назад

Can momentum take a complex value? For position, Ψ*(x)Ψ(x) is pure real because their phases cancel. However, for momentum, I do not see why the equation should yield a real expected value. Love the video!

@alphabetgpt4 3 года назад

Ini adalah pembuktian bahwa semuanya memiliki solusi bagian yg paling bukan

@beehappy5677 3 года назад

6.38 Doesnt the boundary limit apply to x in the first part of the solution of tbe integral? Then, doesnt it produce a infinityxcero indetermination??

@samybrahimi2045 3 года назад

Thanks for helping us to better understanding of quantum mechanics. Can you show us how to do for resolving the schrodinger equation for Hydrogene atom and for other atoms having several electrons with perturbation theory. Thanks again.

@alphabetgpt4 3 года назад

I hate statictic.. 🙄🙄😘😭

@unkownuser1042 2 года назад

Bro what app do you use

@alphabetgpt4 3 года назад

It's odd really...

@subasinidas1711 2 года назад

Sir, please make a video on momentum space wave function

@youssefbourais534 5 лет назад

Good job man ...thanx

@nikitasharma3869 2 года назад

Thank you sir g

@insignificantphysicist1295 6 лет назад

Can you suggest me a good book to study these basics?

@FacultyofKhan 6 лет назад

Griffith's is pretty nice for basic Quantum Mech. I'd start with that if I were you.

@lutfiandre4371 4 года назад

would like you to share what kind of app you used to demonstrated the explanation ?

@neutralgeek9492 6 лет назад

Quite fast but good explanation.

@MonsterIsABlock 4 года назад

turn it on 0.75 then its better

@yashupadhyay50 6 лет назад

sir please give lecture on step potential and particle in one dimensional box

@kipropcollins4220 2 года назад

this got to be the best lesson i have ever attended on QM

@Sairaj922 4 года назад

6:26 , shouldnt the limit be taken with x? But x goes to infinity even though phi goes to 0

@HidekazuOki 6 лет назад

Shouldn't repeated measurement of the same system yield different results based on the probability density of the wavefunction, not the same exact state each time?

@FacultyofKhan 6 лет назад

No, because measuring a system directly interferes with it and collapses the wavefunction (i.e. wavefunction collapse). I'd have to wait for the particle to reach steady state again before I'd get a different measurement based on the probability density of the wavefunction I originally collapsed, as I said in this video.

@aleksandrabobot6739 4 года назад

At 5:16: from where can you notice that?

@manueljenkin95 3 года назад

Thank you very much!

@sanghabalkhande3916 3 года назад

Thank you sir 👍

@anmolperson1441 3 года назад

Thank you sir ❤️

@aclearlight 3 года назад

Nicely done!

@fionachiaraviglio4302 4 года назад

I LOVE KAHN

@reinia127 5 лет назад

thank you so much!!!!

@shyamsunder7819 5 лет назад

How did derivative with respect to t turned to the derivative with respect to x

@FacultyofKhan 5 лет назад

I used the Schrodinger equation to make that conversion. Here is the relevant part from the previous video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-kUm4q0UIpio.html Hope that helps!

@solsticetwo3476 5 лет назад

At 10:30 you are missing a 'X' inside the integral

@kovanovsky2233 4 года назад

the 'X' is in parenthesis between the psi* and psi

@amedeodeamicis1957 4 года назад

i didn't understand....

@paulg444 3 года назад

i disagree, the wave function as described is a function of time. You have implied that you have set up a physical system described by that wave function. If you sample from it (i.e. measure the position) and then repeat ad infinitum to aggregate an ensemble of measurements then the first moment is indeed the mean of the measurements. Speaking about wave function "collapse" in the first 2 minutes of explanation is introducing an interpretation of QM that is completely unnecessary here and it confuses the reader. Think of the wave function as described here as a likelihood function or conditional probability for the measurements system.

@sabuhihasanov9835 3 года назад

Prezident niye eshitmir ki, elbette eshidir. Prezidentin her aile üzvünün bir biznesi var. O hele öz ailesinden bashlasin.... Bu veziyyete getiren mehz prezident ve onun etrafidir... Besdirin da prezidente müraciet etdiniz..