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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| when toggle format | what | by | license | comment | |
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| Aug 1, 2020 at 13:21 | vote | accept | Mr. Palomar | ||
| Aug 1, 2020 at 13:12 | comment | added | Mr. Palomar | Thanks, that makes sense. | |
| Aug 1, 2020 at 12:32 | comment | added | Vercassivelaunos | You can always find a basis of the Hilbert space made up of eigenstates of the Hamiltonian, and you can then just invent a fitting set of operators by specifying how they act on these eigenstates, so yes. Wether they are physically relevant is a different question, though. | |
| Aug 1, 2020 at 11:21 | comment | added | Mr. Palomar | Thanks, I think I'm starting to understand better. Is this situation unique for the hydrogen atom? E.g. if we take an atom with more electrons, is there still a finite set of operators whose eigenvalues uniquely specify a basis of $\mathcal{H}$? (I am aware that the Schrödinger equation for atoms with more electrons cannot be solved in terms of exact formulas, but that doesn't exclude such a basis from existing, I presume.) | |
| Aug 1, 2020 at 11:05 | history | edited | Vercassivelaunos | CC BY-SA 4.0 |
added 431 characters in body
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| Aug 1, 2020 at 10:35 | history | answered | Vercassivelaunos | CC BY-SA 4.0 |