Fock-Darwin spectrum ($E_{n\ell }$)

For a circular two-dimensional parabolic dot in perpendicular magnetic field, orbital levels are $\hslash \Omega (2n+|\ell |+1)\pm \ell \hslash {\omega }_c/2$, with ${\Omega }^2={\omega }_0^2+{\omega }_c^2/4$. The sign depends on the angular-momentum and signed-charge convention. At zero field the shell degeneracy is $q+1$ before spin; Zeeman and interaction terms require separate treatment.