Pseudospectral method based on prolate spheroidal wave functions for semiconductor nanodevice simulation

We solve Schrödinger's equation for semiconductor nanodevices by applying prolate spheroidal wave functions of order zero as basis functions in the pseudospectral method. When the functions involved in the problem are bandlimited, the prolate pseudospectral method outperforms the conventional pseudospectral methods based on trigonometric and orthogonal polynomials and related functions, asymptotically achieving similar accuracy using a factor of π/2 less unknowns than the latter. The prolate pseudospectral method also employs a more uniform spatial grid, achieving better resolution near the center of the domain.