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Mar
29
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
Your edit is very helpful, thanks. Note: it turns out I introduced a sign error in the commutator of the equation I was trying to copy from Wikipedia. It's now fixed, but my typo may have leaked into your answer.
Mar
29
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
Thank you. I'm having trouble distinguishing your answer from yuggib's edit (which has time priority). Is the $t$ vs. $t'$ distinction important? Also, in your last equation, do you mean the full (convective?) time derivative instead of the partial derivative?
Mar
29
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
1) I agree that $dA_H/dt \ne (dA_S/dt)_H$, but I wrote the partial derivative wrt t, $\partial A_H/\partial t=(dA_S/dt)_H$, not the full derivative. In your example, I think the partial derivative applied to $A_H$ would only act on the explicit time dependence ($t^2$), not on $x_H^2$ or $p_H^2$, hence the equality I proposed. 2) My goal is education, not amusement. I don't know if I'm being too picky.
Mar
28
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
@AndrewLedesma, Groan... Thank you. Fixed.
Mar
27
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
Thank you for this answer. Unfortunately, I'm a bit confused by it. 1) On the one hand, your "true" equation looks the same as mine, and different from Wikipedia's. 2) On the other, in your example, it looks like $\partial A_H / \partial t = (dA_S/dt)_H $, which would validate the interpretation that you said "did not really make sense to write". In fact, if this equality holds in general, I would have to concede Wikipedia has it right. Thoughts?
Mar
27
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
Thank you for this answer. I certainly have no problems with the classical equation of motion; it's as rigorous as physics gets, I think. For the quantum version, I've only seen derivations that start with the Schrodinger picture; your "direct replacement" procedure is intriguing. Forgive my skepticism, but do you have any references for it? Thanks.
Mar
10
comment Child-Langmuir Space Charge Law for Non-Zero Cathode Potential (Non-Zero Initial Electron Velocity)
(1) thanks but I'll pass, sorry. (2) In this formulation, the initial electron velocity is just that, an initial condition. Once emitted from the cathode, an electron is accelerated by the local electric field, which is determined by (a) the voltage difference between anode and cathode and (b) the electric field from other emitted electrons (the space charge). The value of the cathode voltage alone is insufficient. (3) Presumably there are different physical assumptions behind the two formulations, but I don't have anything intelligent to say about them.
Feb
1
comment In a positively biased PN junction, where do the injection carriers come from?
If, as you say, you like the answer to your Q1 and Q2, you should accept that post, and then ask Q3 and Q4 in a new question.
Jan
31
comment What experiments compete with BICEP 2, and when are their results expected?
@annav: No. Planck measured dust by looking at multiple frequencies, which BICEP2 couldn't do, and the two organizations have now agreed that the signal BICEP2 observed is just dust.
Jan
31
comment What experiments compete with BICEP 2, and when are their results expected?
@annav: You have now seen a "5 signal signal" go away...
Jan
31
comment How did the Bardeen-Brattain point-contact transistor work?
A free version of Bardeen's Nobel Lecture is available from the Nobel site here: nobelprize.org/nobel_prizes/physics/laureates/1956/… .
Dec
20
comment The status of the BICEP2 'discovery' after Planck 2014
Related: physics.stackexchange.com/q/103951
Dec
4
comment Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT
@ZhengLiu, you're welcome. Yes, the basis $\beta$ is orthonormal in the sense of eq. 2.5.19. $N(p)$ must be different from 1 because the argument of the delta-function changes from the standard momentum $k$ (in eq. 2.5.5 and 2.5.14) to an arbitrary momentum $p$ in eq. 2.5.19. The text between eqns 2.5.14 and 2.5.19 works out the proportionality factor between these two delta-functions, and $N(p)$ is selected to cancel that factor.
Nov
7
comment Feynman's proof for Liénard-Wiechert's potential of a moving charge
@guillefix, think I got it. Thanks again for the catch.
Nov
6
comment Feynman's proof for Liénard-Wiechert's potential of a moving charge
@guillefix, thanks! I see now I got sloppy with $c$ in a couple places. (I understand better now why people set $c=1$!) I will patch it today or tomorrow. (I think I need more time than I've got right now, to avoid making another goof.)
Nov
5
comment Where's the energy in a boosted capacitor?
OK I see what you're doing. I should have read your post and previous comments more carefully before commenting; I see you've explained all this before. Sorry. Thanks for being patient.
Nov
4
comment Where's the energy in a boosted capacitor?
I think your argument is undermined by an incorrect formulation of the field energy: $\int T^{00} d^3x$ is not covariant. It should be $\int T^{0 \nu} n_\nu (\gamma d^3x)$.
Oct
31
comment Is there an intuitive explanation for why Lorentz force is perpendicular to a particle's velocity and the magnetic field?
@RobJeffries, Nice! Thanks for the info. "Nulling" set-ups are very attractive; er, well, you know what I mean...
Oct
28
comment Perceived acceleration in an artificially modulated gravitational field
@Hypnosifl, I think the thing about tidal forces is you need (at least) two particles separated in space-time, and the tidal forces decrease with the separation. (That's why I specified a "test particle".) You're right that the proverbial astronaut falling into a black hole will be spaghetti-fied.
Oct
28
comment Perceived acceleration in an artificially modulated gravitational field
@DavidHammen, more's the pity. It seems like one of those things that just ought to be true (imho).