Timeline for When studying the hydrogen atom, why do we seek simultaneous eigenfunctions of $\hat{L}^2$, $\hat{L}_z$, and $\hat{H}$?
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| Aug 1, 2020 at 10:42 | comment | added | Vercassivelaunos | Counterexample: take any two states with same quantum number $n$ but different quantum number $l$. Their linear combination will still be an energy eigenstate , but not an angular momentum eigenstate. | |
| Aug 1, 2020 at 10:39 | comment | added | DoeJohn | "all eigenfunctions must be simultaneously eigenfunctions of angular momentum". This is incorrect. They do not are necessarily simultaneous eigenfunctions. Rather, there exists a basis of such simultaneous eigenfunctions, which is particularly convenient. But that is not the only possible basis made of energy eigenstates. | |
| Aug 1, 2020 at 10:06 | history | answered | my2cts | CC BY-SA 4.0 |