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22h
reviewed Reject If I switch on a generator connected to an open circuit, are the charges oscillating along wires?
22h
accepted Is the Wikipedia version of the Heisenberg equation of motion correct?
1d
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.
1d
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?
1d
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.
1d
comment Is the Wikipedia version of the Heisenberg equation of motion correct?
@AndrewLedesma, Groan... Thank you. Fixed.
1d
revised Is the Wikipedia version of the Heisenberg equation of motion correct?
Fix commutator order.
Mar
27
awarded  Yearling
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
26
asked Is the Wikipedia version of the Heisenberg equation of motion correct?
Mar
22
reviewed Reject Two balls travelling at different speeds collide in two referentials
Mar
21
reviewed Reject Rough/ballpark thermodynamics and black body temperature question
Mar
18
reviewed Approve Could we send a man safely to the Moon in a rocket without knowledge of general relativity?
Mar
18
reviewed Approve Why doesn't the potential drop as a $E=\nabla V$ inside a circuit when there is no resistor?
Mar
16
reviewed Approve Applying rotation operator to spin
Mar
13
reviewed Approve Why are stars white?
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.
Mar
10
reviewed Reject Is Stephen Wolfram's NKS, an attempt to explain the universe with cellular automata, in conflict with Bell's Theorem?
Mar
10
reviewed Reject Is Stephen Wolfram's NKS, an attempt to explain the universe with cellular automata, in conflict with Bell's Theorem?