Confined states in ellipsoidal quantum dots

We study the motion of a particle confined in an ellipsoidal quantum dot, solving the corresponding Schrodinger equation both numerically, using the appropriate coordinate system, and variationally. The results from the two methods are compared, varying the ellipsoid semi-axes. We find that the confined-state energies split with respect to those of the spherical quantum dot and this can be explained as a consequence of both a volume-induced deformation effect and a geometry-induced one. The role of the dot geometry is shown to be relevant also for the formation of topological surface states.