Stark effect in the optical absorption in cubical quantum boxes

We have calculated the effect of a transverse electric field on the ground and the first few excited states of the electrons confined in a cubical quantum box and used these results to examine the effect of the electric field on the intersubband optical absorption in such quantum boxes. The electric field removes the degeneracies between several of the excited states in the box, which leads to peaks in the intersubband optical absorption of the box. The application of the electric field leads to a Stark shift of the electron energies, which is quadratic in the field at low fields but becomes almost linear in the field at high fields. The application of the electric field leads to a decrease in the energy levels. The electric field shifts the peaks in the optical absorption spectrum of the cubic box in a manner that depends upon the polarization of the optical field with respect to the applied electric field. We compare the results we obtain using the expansion of the wave functions in terms of the eigenstates of the particle in the box to the exact analytical results using Airy functions and find excellent agreement using only a few terms in the expansion. This has implications for results obtained using the expansion method when we do not have exact solutions with which to make a comparison.