Timeline for Orthonormal basis of eigenvectors of Hamiltonian - Is there any theorem justifying the physicist approach?
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5 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2022 at 20:52 | comment | added | Abdelmalek Abdesselam | See mathoverflow.net/a/278598/7410 | |
| Apr 22, 2022 at 20:49 | comment | added | Abdelmalek Abdesselam | @MathMath: It seems you want Schrodinger operators which are (essentially) self-adjoint as well as with compact resolvent. TYpically you need a potential V that grows fast enough so eigenstates are trapped, i.e., square integrable. You can search with keywords like: Schrodinger operators with confining potential, compact resolvent., and probably find useful references. | |
| Apr 22, 2022 at 19:58 | comment | added | Carlo Beenakker | see mathoverflow.net/q/383952/11260 for a discussion of this issue | |
| Apr 22, 2022 at 19:40 | comment | added | Andreas Blass | Lots of physical systems have observables with a continuous spectrum (possibly in addition to a point spectrum), for example the Hamiltonian in the case of scattering states (as opposed to bound states). The formalism of "rigged Hilbert spaces" provides eigen"vectors" for elements of the continuous spectrum, but these are not in the Hilbert space. They may be distributions, or unnormalizable plane waves, or other stuff. | |
| Apr 22, 2022 at 19:06 | history | asked | MathMath | CC BY-SA 4.0 |