Numerical implementation of the ellipsoidal wave equation and application to ellipsoidal quantum dots

We present a full implementation of the algorithm of Arscott et al. [Math. Comp. 40 (1983) 367] in order to evaluate the discrete eigenvalue spectrum and associated eigenfunctions of the Laplacian operator in a three-dimensional ellipsoidal region subject to Dirichlet boundary condition. The results were applied to provide the first solution to the triaxial ellipsoidal infinite-barrier quantum-dot problem in quantum mechanics.