Convenient and simple numerical techniques for performing quantum computations based on matrix
representations of Hilbert space operators are presented and illustrated by various examples. The
applications include the calculations of spectral and dynamical properties for one-dimensional and
two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems.
Due to their technical simplicity these methods are well suited as a tool for teaching quantum
mechanics to undergraduates and graduates. Explicit implementations of the presented numerical
methods in Matlab are given.