 Flux-threaded quantum rotor

For the Gaussian-unit flux term $e{\Phi }_B\dot{\varphi }/(2\pi c)$, canonical momentum is shifted by $e{\Phi }_B/(2\pi c)$. Periodic wavefunctions then give the displayed spectrum for integer $n$. The flux period is $hc/|e|$ in these units; the corresponding SI expressions omit $c$. A gauge change transfers the flux to a twisted boundary condition rather than removing it from the physical problem. Half-integer $f$ gives a pair of degenerate nearest-momentum levels.