Timeline for Explicitly verifying a scattering theory identity
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2018 at 10:15 | vote | accept | Wolpertinger | ||
| Oct 26, 2018 at 1:25 | answer | added | user200143 | timeline score: 5 | |
| S Sep 13, 2018 at 16:00 | history | bounty ended | CommunityBot | ||
| S Sep 13, 2018 at 16:00 | history | notice removed | CommunityBot | ||
| Sep 6, 2018 at 8:24 | history | edited | Wolpertinger | CC BY-SA 4.0 |
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| Sep 5, 2018 at 14:32 | history | edited | Wolpertinger | CC BY-SA 4.0 |
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| S Sep 5, 2018 at 14:05 | history | bounty started | Wolpertinger | ||
| S Sep 5, 2018 at 14:05 | history | notice added | Wolpertinger | Draw attention | |
| S Aug 27, 2018 at 1:00 | history | bounty ended | CommunityBot | ||
| S Aug 27, 2018 at 1:00 | history | notice removed | CommunityBot | ||
| Aug 25, 2018 at 8:43 | comment | added | Wolpertinger | @TwoBs might be an option, do you think you can actually show how the identity is fulfilled with that approach? Just one word of warning: I suspect this won’t work either. Reason: I didn’t define the S-matrix via relative coefficients, but via the proper overlap integral. I know its form from an entirely different calculation and the relative coefficient in what i called psi^+ happens to be the same. | |
| Aug 24, 2018 at 20:06 | comment | added | TwoBs | Not sure, another way (orthogonal to my previous comment :-) ) is perhaps to change your definition of the S-matrix and call $S$ the relative coefficient of free solutions on the half-line $(-L,+\infty)$ (rather than on the whole line) that are needed to reproduce the case with $V_0\neq 0$. So that both with $V_0=0$ and $V_0\neq 0$ the wave functions satisfy proper BC's at $x=-L$. | |
| Aug 24, 2018 at 9:09 | comment | added | Wolpertinger | @TwoBs nevertheless I think you are on the right track!! Especially because if you look at the form of the $\psi^{(+)}$ state, asymptotically you get the $e^{\pm i\sqrt{2E}x}$ states with the relative magnitude being the scattering matrix. Due to the above arguments my suspicion is, however, that the free state might be correct and the $\psi^{(+)}$ state wrong. I do not want to exclude either option though. | |
| Aug 24, 2018 at 9:05 | comment | added | Wolpertinger | @TwoBs That is a great idea! To clarify, would you use something like $\psi_0(E,x) \propto e^{\pm i\sqrt{2E}x}$? I actually tried these before and have 3 problems with it: a) I can't get it to give a T-matrix that fulfills the relation to the S-matrix. b) From an abstract point of few I think this would give a non-unitary S-matrix for reflection, since can not avoid opening the transmission channel if you use these solutions. c) I think that instead of an infinite potential at $x<-L$ you could also consider a boundary condition at $x=-L$. And the free states should adhere to the BCs... | |
| Aug 24, 2018 at 8:52 | comment | added | TwoBs | As a tentative resolution, I would think that you should be using actual free solutions (plane waves) where the whole potential, not just $V_0$, is removed. In other words, the S-matrix isn't defined with respect to the free propagation on the whole real line, rather than just a semi-line? Incidentally, the free wave should have the same energy of the exact solution. | |
| Aug 19, 2018 at 10:59 | history | edited | Wolpertinger | CC BY-SA 4.0 |
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| Aug 19, 2018 at 0:02 | history | tweeted | twitter.com/StackPhysics/status/1030968232956645381 | ||
| S Aug 18, 2018 at 23:38 | history | bounty started | Wolpertinger | ||
| S Aug 18, 2018 at 23:38 | history | notice added | Wolpertinger | Draw attention | |
| Aug 16, 2018 at 14:57 | history | asked | Wolpertinger | CC BY-SA 4.0 |