Timeline for If there are eigenstates of $L_z$ in a degenerate subspace, are there also eigenstates of $L^2$?
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| Jun 16, 2019 at 20:29 | comment | added | Cosmas Zachos | $L_z$ is the only symmetry of your system: the full spherical symmetry πΏβ, and hence $πΏ^2$ simply do not commute with the potential, so you could probably never consider them profitably. That is, the generators πΏπ₯, πΏπ¦ are badly broken in your system, much unlike in the 3D oscillator. The representation structure of SO(2) and SO(3) are very different, so it is not apparent what puzzles you... | |
| Jun 16, 2019 at 9:51 | history | edited | Qmechanic♦ |
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| Jun 16, 2019 at 9:39 | history | asked | neverneve | CC BY-SA 4.0 |