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Monodromy-free Schrödinger operators with quadratically increasing potentials

A. A. Oblomkov

M. V. Lomonosov Moscow State University

Abstract: We consider one-dimensional monodromy-free Schrödinger operators with quadratically increasing rational potentials. It is shown that all these operators can be obtained from the operator $-\partial^2+x^2$ by finitely many rational Darboux transformations. An explicit expression is found for the corresponding potentials in terms of Hermite polynomials.

Received: 23.03.1999

DOI: 10.4213/tmf817

 English version: Theoretical and Mathematical Physics, 1999, 121:3, 1574–1584

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