Infinite-well interband selection rule

In an infinite square well, electron and hole envelopes are the same normalized sine functions even when their effective masses differ. In the electric dipole and envelope approximations, their overlap is $\int F_{n^{\prime }}^{\ast }(z)F_n(z)dz={\delta }_{n^{\prime }n}$. The same-index rule is an ideal-envelope rule, separate from Bloch-state polarization selection rules.