Timeline for Time Evolution of Wigner Function
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2022 at 8:45 | comment | added | eeqesri | @MrProof I am not an expert in QM but pretty much any book on QM should be able to explain it. As far as I know the commutator is something like a Poisson bracket in classical mechanics. The commutator is also important for deriving the Heisenberg's uncertainty principle. Hope that helps. | |
| Feb 2, 2022 at 8:42 | comment | added | Mr. Proof | @eeqesri I was meaning the commutator in general where does it come from Indy Schrodinger equation and in Hatree equation. I’m a mathematician and I’m not familiar with the derivations of these equations. | |
| Feb 2, 2022 at 8:39 | comment | added | eeqesri | @MrProof Do you mean how the commutator gets mapped to the moyal bracket? | |
| Feb 2, 2022 at 8:03 | comment | added | Mr. Proof | @eeqesri Could you explain for me (or show me some references) where the commutator originally came from? | |
| Sep 30, 2020 at 3:01 | vote | accept | eeqesri | ||
| Sep 30, 2020 at 3:00 | history | edited | eeqesri | CC BY-SA 4.0 |
completed the solution
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| Sep 29, 2020 at 17:13 | comment | added | eeqesri | I think I got it now. I will update the solution tomorrow. | |
| Aug 22, 2020 at 16:39 | comment | added | ZeroTheHero | The Moyal bracket of two functions $W_A\star W_B-W_B\star W_A$ is the Poisson bracket $\hbar\{W_A,W_B\}_P$+ correction terms (here, this is an expansion in the semi-classical parameter $\hbar$). The extra pieces in the $\star$ product will eventually subtract to produce a "non-classical" part to the evolution. | |
| Aug 22, 2020 at 15:35 | comment | added | eeqesri | How can one actually understand higher orders of this special derivative $\Lambda$? | |
| Aug 22, 2020 at 12:44 | comment | added | ZeroTheHero | There are a lot of details in that paper I referenced. | |
| Aug 22, 2020 at 12:06 | comment | added | eeqesri | I thought about it again. Intuitively higher order terms I think must vanish, because the Weyl transformed Hamiltonian is quadratic in $x$ and $p$, however the next order involves derivatives of third order, so those should vanish I guess, but I'd have to do an exact calculation. | |
| Aug 22, 2020 at 10:10 | comment | added | eeqesri | @ZeroTheHero thanks I will take a look | |
| Aug 21, 2020 at 14:38 | comment | added | ZeroTheHero | Yes you might want to have a look at: Hillery, M.O.S.M., O'Connell, R.F., Scully, M.O. and Wigner, E.P., 1984. Distribution functions in physics: fundamentals. Physics reports, 106(3), pp.121-167, in particular Eq.(2.54). This link: citeseerx.ist.psu.edu/viewdoc/… gives me open access but it might not work for you. I might not be what you want and unfortunately I'm pressed for time... | |
| Aug 21, 2020 at 14:13 | comment | added | eeqesri | @ZeroTheHero does it really? Do you have any references? | |
| Aug 21, 2020 at 12:55 | comment | added | ZeroTheHero | If I recall correctly, the series on the right will truncate for the h.o. | |
| Aug 21, 2020 at 10:54 | history | answered | eeqesri | CC BY-SA 4.0 |