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

Eremenko, Alexandre; Gabrielov, Andrei; Shapiro, Boris

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

Authors

Eremenko, Alexandre

Gabrielov, Andrei

Shapiro, Boris

Description

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