Timeline for Non-degeneracy of ground state in quantum mechanics
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2010 at 18:03 | comment | added | Tim van Beek | That's tricky! Allow some handwaving: If the potential goes to $\infty$ that means particles are confined to a bounded region (the probability to find them outside is very low/ can be made arbitrarily low). In a bounded region in classical physics there can be different locations which minimize the potential energy, but in quantum mechanics the ground state describes the probability to find it in any of those -> therefore it is unique in QM. But note that you can get degenerate ground states by dropping the other assumption on V ($V \in L^2_{loc}$). | |
| Jun 4, 2010 at 17:02 | comment | added | Jamie Vicary | Do you have any insight into what role unboundedness of the potential plays? I mean physically, rather than mathematically? | |
| Jun 4, 2010 at 15:41 | vote | accept | Onkar | ||
| Jun 4, 2010 at 15:42 | |||||
| Jun 4, 2010 at 13:19 | history | edited | Tim van Beek | CC BY-SA 2.5 |
added 159 characters in body
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| Jun 4, 2010 at 13:09 | history | answered | Tim van Beek | CC BY-SA 2.5 |