Timeline for Schrödinger equation approximation – continuity of eigenvalues with respect to potential
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2023 at 22:53 | history | edited | Willie Wong |
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| Mar 18, 2023 at 14:11 | comment | added | Rohan Didmishe | I see, thank you for your inputs. | |
| Mar 18, 2023 at 13:40 | comment | added | Michael Engelhardt | Denoting the unperturbed potential by $V_{\epsilon } $ is maximally confusing here. Write $V=V_0 + \epsilon V' $ with the $V_0 $ problem solvable and develop the perturbation series in $\epsilon $. Unless there are degeneracies in the spectrum of the $V_0 $ problem, the spectrum of the $V$ problem can indeed be written as a power series in $\epsilon $. | |
| Mar 18, 2023 at 11:16 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 18, 2023 at 11:13 | comment | added | Rohan Didmishe | Well in this case there is no parameter valued expansion I am assuming a-priori; is that the only case in which some scheme like this can be justified? @CarloBeenakker | |
| Mar 18, 2023 at 11:11 | comment | added | Rohan Didmishe | Thank you for your comment; could you also provide a source for such an analysis? With respect to how the error terms could be controlled | |
| Mar 18, 2023 at 11:08 | comment | added | Carlo Beenakker | isn't this just what we try to achieve with perturbation theory? assuming the ground state is not degenerate, the correction $\delta E=E-E_\epsilon$ equals $\int (V-V_\epsilon)|\Psi_\epsilon|^2 d^3 r$ plus terms of order $\epsilon^2$ (with $E_\epsilon$ and $\Psi_\epsilon$ the ground state eigenvalue and eigenfunction in the potential $V_\epsilon$) | |
| S Mar 18, 2023 at 11:02 | review | First questions | |||
| Mar 18, 2023 at 11:42 | |||||
| S Mar 18, 2023 at 11:02 | history | asked | Rohan Didmishe | CC BY-SA 4.0 |