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

High Energy Eigenfunctions of One-Dimensional Schrödinger Operators with Polynomial Potentials