Timeline for Proof the solution of von Neumann equation will fluctuate forever if Hamiltonian and initial density matrix does not commute
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 22, 2014 at 14:21 | comment | added | Carlo Beenakker | $\rho(t)=U(t)\rho(0)U^{\dagger}(t)$ where $U(t)=e^{-iHt}$ has matrix elements $e^{-iE_n t}\delta_{nm}$ in the eigenbasis of $H$. | |
| Aug 22, 2014 at 13:30 | comment | added | Xingdong Zuo | Thank you for the answer. When it comes to the form with the energy eigenvalues $\exp(-i(E_m - E_n))t$, is it still possible to consider it as an operator such that $U'(t, 0) = \exp(-i(E_m - E_n))t \neq I$, where $I$ denotes the identity operator. Or we can only simply say $\exp(-i(E_m - E_n))t \neq 1$ ? | |
| Aug 22, 2014 at 12:07 | vote | accept | Xingdong Zuo | ||
| Aug 22, 2014 at 11:16 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |