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Oct
20
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Oct
20
awarded  Scholar
Oct
20
awarded  Supporter
Jul
22
awarded  Nice Question
Mar
1
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Dec
13
comment Greiner or Landau for Math major student?
Can I say that if I mainly consult this 2 series, then I do not really need to use like Goldstein, Jackson for "main-reading" anymore ? (Maybe just occasionally for some pages in library) (And physics is not core research for me after all, though it is important and often related for my research field)
Dec
13
comment Greiner or Landau for Math major student?
Thanks for the advice. Yeah, I agree that it is necessary to consult many resources, one of main purpose here is to select a "main" good resource for personal collection and serious study, then it is ok to use the library for filling the gaps.
Dec
13
asked Greiner or Landau for Math major student?
Oct
20
accepted Solution of dynamics of density matrix
Sep
24
awarded  Autobiographer
Aug
22
comment Stabilization of von Neumann equation
Thank you very much. Now I understand. By the way, is it called stationary state in physics ?
Aug
22
comment Stabilization of von Neumann equation
I agree with it that for the closed quantum system it will endlessly oscillate. Well, I'd like to know if it is possible to explicitly to show $[H, \rho(0)]\neq 0$ in your proof of the form of expansion of density operator above, i.e. $$ \rho(t) = \sum_{m,n} \rho_{mn}(0) e^{-iHt}\lvert m\rangle\langle n\rvert e^{-iHt} = \sum_{m,n} \rho_{mn}(0) e^{-i(E_m-E_n)t}\lvert m\rangle\langle n\rvert = \sum_{m,n} \rho_{mn}(t) \lvert m\rangle\langle n\rvert,$$
Aug
22
comment Stabilization of von Neumann equation
Yes, and in the solution function graph the fluctuation of the curve to be smaller and smaller as time to infinity. The point is not against the proof with the eigenstates, but the place where we can use the condition that $H$ and $\rho(0)$ does not commutes, since the the form above can always be shown even if $[H, \rho(0)]=0$
Aug
21
comment Stabilization of von Neumann equation
Thank you for the solution. But I am not very sure where it was used the condition $[H, \rho(0)]\neq 0$ to prove that the solution $\rho(t)$ will be stabilized, where it is not related to the zero derivative, since there can be small fluctuation even with large derivative.
Aug
16
accepted Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes
Aug
16
comment Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes
@yuggib It means the density matrix will never approach the steady state.
Aug
16
revised Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes
added 53 characters in body
Aug
16
revised Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes
deleted 1 character in body
Aug
16
asked Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes
Jun
3
accepted Derivation of a quantum dynamical map on open quantum system