Numerical Calculations of the Quantum States in Semiconductor Nanostructures

In this review we describe the use of a powerful numerical tool to obtain quantum states of semiconductor nanostructures. A detailed account of the numerical method is given and the method is applied to solve the Schrödinger equation for several semiconductor systems within the effective mass approximation. The variety of systems investigated shows how flexible and effective the method is. The scheme for the calculation of the eigenvalues and eigenvectors is a modified version of a split-operator approach to propagate the wave functions by infinitesimal time steps, applied both in real and imaginary time propagations. Interesting aspects in this modified approach are the use of real space coordinates, time propagation in real and imaginary domains, the treatment of excited states as well as of systems with interacting particles.