Schrödinger Operators with Moving Point Perturbations and Related Solvable Models of Quantum Mechanical Systems

Abstract

A class of explicitly solvable models including those of low-dimensional systems in a magnetic field is considered. The spectral analysis of these models is reduced to the investigation of the spectrum of an ordinary differential operator perturbed by a point potential with varying support. The complete analysis of the variation of the eigenvalues and elgenfunctions with position of the potential support is given.