I would like to know if the exact ground state of a closed-shell atom or molecule can have a spatial degeneracy. If we ignore relativistics effects, the Hamiltonian of the system $H$ commutes with the Spin operators $S^{2}$ and $S_{z}$, so, to each eigenstate of $H$, there are another $2S + 1$ eigenstates that have the same energy. In the case of a closed-shell system, $S = 0$ and there are no spin degeneracy. However, my doubt is about spatial degeneracy, that is, if it can exist two states $\Psi$ and $\Psi'$ with the same energy eigenvalue that have the same spin. (in this case, $H$ is the full Hamiltonian, that includes electron-electron interaction)

  • $\begingroup$ The nearest to your requirement would seem to be a particle on a ring where $\psi(\theta)=e^{\pm ni\theta}/\sqrt{2\pi}$ and where $n=0,\pm1,\pm2\cdots$ and when $n>0$ $\endgroup$
    – porphyrin
    Jul 11, 2020 at 14:25


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.