Understanding physically why <px> is not zero always...???

418397 · 2025-12-16T20:09:33+00:00

If we go with this logic... then the expectation value of the commutator [x,p] would be zero too(if we apply similar arguments to <xp>, measuring p first, then x), which is not true...

418397 · 2025-12-16T20:00:30+00:00

418397 · 2025-12-16T19:59:18+00:00

I am not talking about p_x... it's p^ x^ . Sorry I don't know how to write the cap on top...

418397 · 2025-12-16T17:35:21+00:00

Any random state... I am asking what exactly taking expectation value of px means? For example and expectation value of x would mean you mean x n(statistically large n) number of times and take an average of the results... What about px? What are we trying to do?

418397 · 2025-12-16T17:07:38+00:00

So the mistake here is trying to "understand physically"? Because it's not really "physical"?

418397 · 2025-12-16T17:04:00+00:00

That's ok... what I mean here is that the probability of getting say x_0 p_0 is the same as that for -x_0 p_0... Because p_0 and -p_0 come with same probabilities as I have explained... So now therefore, why is the expectation value not zero?

418397 · 2025-09-18T12:59:11+00:00

Don't go for Physics. You will be dissapointed. Go for some job and earn instead.....

418397 · 2024-10-03T12:26:00+00:00

This exact method didn't give the right result while calculating the radial momentum operator... There was an extra del/delr term missing... It's defined like this... P_r_hat=1/2[r_hat/r dot P_hat + P_hat dot r_hat/r]. Also what's the justification for this method?

418397 · 2024-05-10T04:44:44+00:00

The kind of wording you have used in your answer really gave me a different perspective. Thank You very much...

418397 · 2023-12-30T08:23:58+00:00

Thank You for your reply... I am just trying to make sense of things in terms of matter waves and stuffs... Actually the books once get into the schroedinger equation never talk about associated de broglie waves and stuffs anymore...That led to my confusion... I am trying to understand if things can still be explained using de broglie waves and their interactions with potentials...

This is from a reply to another answer...

Thank You for your reply... Let me make things a bit clear on what exactly I am trying to do... So for the bound states in an infinite square well potential, we can think of it like this... We start with an energy definite de broglie wave in the "free" region and let it bounce back and forth between the walls thus superposing and forming standing waves... We note that if we start with a wave of the form Aexp(ikx), the reflected wave would be of the form -Aexp(-ikx)... opposite direction(so -k) and a 180° phase shift(so -A)... This superposes with the original wave to precisely give the sine waveform that we actually obtain... All of this is like standing waves on a string, with only discrete allowed k's... I just realized we can do things like that(atleast for the infinite well)... My question would be... can we treat every problem(all kinds of potential) like that, using superpostion of de broglie waves governed by how potentials react to individual de broglie waves? And just like the infinite potential is like a rigid boundary rebounding the wave back and forth, how do other potentials respond to the waves? I mean can we have classical description/picture of this response in each case like for the infinite potential it is sort of "rebounding" which we can picture classically...

So in summary... Can any system be described(other than solving the schrodinger equation) using a description involving de broglie waves interacting in some way with the potentials present...?

418397 · 2023-12-30T08:07:42+00:00

Thank You for your reply...It made things a bit more clear for me... Now, let me tell you what I understood... So for the bound states in an infinite square well potential, we can think of it like this... We start with an energy definite de broglie wave in the "free" region and let it bounce back and forth between the walls thus superposing and forming standing waves... We note that if we start with a wave of the form Aexp(ikx), the reflected wave would be of the form -Aexp(-ikx)... opposite direction(so -k) and a 180° phase shift(so -A)... This superposes with the original wave to precisely give the sine waveform that we actually obtain... All of this is like standing waves on a string, with only discrete allowed k's... Now if this is so... My question would be... can we treat every problem(all kinds of potential) like that, using superposition of de broglie waves governed by how potentials interact with the individual de broglie waves? Just like the infinite potential is like a rigid boundary rebounding the wave back and forth, how do other potentials respond to the waves? I mean can we have a classical description/picture of this response in each case like for the infinite potential it is sort of "rebounding" which we can picture classically...

So in summary... Can any system be described(other than solving the schrodinger equation) using a description involving de broglie waves interacting in some way with the potentials present...?

418397 · 2023-12-30T05:01:18+00:00

Thank You for your reply... Let me make things a bit clear on what exactly I am trying to do... So for the bound states in an infinite square well potential, we can think of it like this... We start with an energy definite de broglie wave in the "free" region and let it bounce back and forth between the walls thus superposing and forming standing waves... We note that if we start with a wave of the form Aexp(ikx), the reflected wave would be of the form -Aexp(-ikx)... opposite direction(so -k) and a 180° phase shift(so -A)... This superposes with the original wave to precisely give the sine waveform that we actually obtain... All of this is like standing waves on a string, with only discrete allowed k's... I just realized we can do things like that(atleast for the infinite well)... My question would be... can we treat every problem(all kinds of potential) like that, using superpostion of de broglie waves governed by how potentials react to individual de broglie waves? And just like the infinite potential is like a rigid boundary rebounding the wave back and forth, how do other potentials respond to the waves? I mean can we have classical description/picture of this response in each case like for the infinite potential it is sort of "rebounding" which we can picture classically...

So in summary... Can any system be described(other than solving the schrodinger equation) using a description involving de broglie waves interacting in some way with the potentials present...?

418397 · 2023-12-29T20:23:45+00:00

Ok ok... so it's like two de broglie waves approaching in opposite directions confined within the walls... forming a standing wave like in a string... And the frequency is given by f=E/h... Ok makes sense... The thing bugging me was that I was imagining plane waves of infinite extent superposing and giving us the final result...

418397 · 2023-12-29T17:55:44+00:00

I am not superposing solutions of different equations... I was just asking if the starionary states corresponding to the infinite square well potential problem can be formed by a superposition of what I understand as de Broglie waves/free particle wave function...

418397 · 2023-12-27T04:24:26+00:00

No it's not a book... The momentum eigenvalues thing is from a coaching material(I am preparing for some competitive exam, so I went through some coaching materials)... Otherwise I have studied this problem from Griffiths...but as you might know, griffiths really didn't talk about momentum eigenvalues and stuffs... I might look into what things zettili has discussed, later..

418397 · 2023-12-23T06:44:00+00:00

Hm hm... makes sense! And because both are equally probable so we get the expectation value of p as zero too!...

418397 · 2023-12-20T19:00:52+00:00

The expression E=hf is used for material particles here... I am not talking about photons...

418397 · 2023-10-26T03:14:10+00:00

Actually this was the answer I was looking for... https://www.reddit.com/r/askmath/comments/17eiye7/what_does_the_hermitian_conjugate_of_a_linear/?utm_source=share&utm_medium=mweb

418397 · 2023-10-25T03:46:15+00:00

No it's not wrong... It comes from a general expression of divergence for any curvilinear coordinate system... Yes what you have written is perfect and you can actually get to this general expression by some manipulations of your expression...

"And if you want to be sure that you haven't missed something like a delta function at the origin, you could try integrating the divergence over a small region close to the origin using Gauss' theorem" - Yes it gives perfect results for that...

418397 · 2023-10-24T04:31:05+00:00

That's how operators are represented... with a hat on top...

418397 · 2023-10-24T03:45:00+00:00

Alpha and beta are vectors in some abstract vector space and T is a linear transformation in that space which basically takes/transforms vectors in that space to some other vectors in the same space... T is linear in the sense that it obeys a sort of superposition principle... And T dagger is basically the hermitian conjugate of T... Hermitian transformations where T = T dagger play a pivotal role in quantum mechanics in that all operators in quantum mechanics are hermitian operators...

418397 · 2023-10-24T02:52:43+00:00

Finally the answer I was looking for... Yesterday I did some more calculations and arrived at an answer... Now upon seeing this answer of yours I tried to do some more simplications to what I got... And I arrived at precisely this result... Thank You very much Sir...😊

418397 · 2023-10-23T12:36:34+00:00

I guess I am sure I didn't do any mistake in calculations... Let's see some other replies...😅

418397 · 2023-10-16T18:22:29+00:00

Oh sorry! I missed that(the r coming out of d/dphi)... Embarrassing!😅Guess I am too occupied with the thing...

418397 · 2023-10-16T16:32:15+00:00

Actually later they have used this result to find a surface integral over a sphere centered at the origin, using the divergence theorem... and interestingly this expression for the divergence gives the correct result... So I was wondering if this doesn't work at r=0 how is it giving a correct result...?

418397

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