It is possible to construct two-dimensional quantum tubes by composing a semiconductor of several materials, i.e., a quantum heterostructure, see figure. These semiconductors are used in computers and some dimensions may be so small that quantum effects become important. We analyse such quantum tubes, modelled with an effective square potential, using operator methods. Of particular interest is to determine the bound states. The purpose is to develop reliable mathematical and numerical methods. Numerical stability, in particular, is a critical issue.

Schematic of heterostructure and split-gate structure