Position and Momentum from Wavefunctions | Quantum Mechanics

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.

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[_DD_]

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!

[medtabernoust]

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 <3

[julianandresflorezsolano]

This is 10 times better than the lectures my professor gives

[kipropcollins]

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

[munish]

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...

[ostensiblyquerulous]

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

[novocaine]

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!

[samybrahimi]

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.

[subasinidas]

Sir, please make a video on momentum space wave function

[atwellbill]

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 << c, is not true??

[bikashbora]

Please make an video on Schrödinger and Heisenberg interaction pictures

[fosheimdet]

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

[lutfiandre]

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

[dailydoorsteprangoli]

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

[beehappy]

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??

[yashupadhyay]

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

[insignificantphysicist]

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

[arhaankhan]

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

[HidekazuOki]

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?

[Sairaj]

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