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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 1, 1998, pp. 37–55
DOI: 10.4171/ZAA/807

Published online: 1998-03-31

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

V.A. Geyler[1] and I.V. Chudaev[2]

(1) Ogarev University Mordovia, Saransk, Russian Federation
(2) Ogarev University Mordovia, Saransk, Russian Federation

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.

Keywords: Schrödinger operators, point perturbation, low-dimensional systems in a magnetic field, impurity in a well

Geyler V.A., Chudaev I.V.: Schrödinger Operators with Moving Point Perturbations and Related Solvable Models of Quantum Mechanical Systems. Z. Anal. Anwend. 17 (1998), 37-55. doi: 10.4171/ZAA/807