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Beschreibung:
In the physics of layered semiconductor devices the k · p method in combination with the envelope-function approach is a well established tool for band structure calculations. We perform a rigorous mathematical analysis of spectral properties for the corresponding spatially one dimensional k · p Schrödinger operators; thereby regarding a wide class of such operators. This class covers many of the k · p operators prevalent in solid state physics. It includes k · p Schrödinger operators with piecewise constant coefficients which is a prerequisite for dealing with the important case of semiconductor heterostructures. We also introduce a regularization of the problem which gives rise to a consistent discretization of k · p operators with jumping coefficients and describe our toolbox KPLIB for the numerical treatment of k · p operators. In particular we address the question of persistence of a spectral gap over the wave vector range.