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

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.

22 pages, 9 figures

References in corpus (1)

• Schrödinger type eigenvalue problems with polynomial potentials: Asymptotics of eigenvalues