Confined states in ellipsoidal quantum dots

We study the motion of a particle confined in an ellipsoidal quantum dot, s olving the corresponding Schrodinger equation both numerically, using the a ppropriate coordinate system, and variationally. The results from the two m ethods are compared, varying the ellipsoid semi-axes. We find that the conf ined-state energies split with respect to those of the spherical quantum do t and this can be explained as a consequence of both a volume-induced defor mation effect and a geometry-induced one. The role of the dot geometry is s hown to be relevant also for the formation of topological surface states.