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High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials

Alexandre Eremenko·Andrei Gabrielov·Boris Shapiro
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Abstract

For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the eigenvalues tend to infinity. This limit distribution depends only on the degree of potential and on the boundary conditions.

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Alexandre Eremenko, Andrei Gabrielov, Boris Shapiro. 2007-03-14. High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials. https://arxiv.org/abs/math-ph/0703049

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