Computational Methods and Function Theory 8 (2008), No. 2, 513--529
Copyright Heldermann Verlag 2008
Alexandre Eremenko
eremenko@math.purdue.edu , Purdue University, Department of Mathematics, West Lafayette, IN 47907 U.S.A.
Andrei Gabrielov
agabriel@math.purdue.edu , Purdue University, Department of Mathematics, West Lafayette, IN 47907 U.S.A.
Boris Shapiro
shapiro@math.su.se , Stockholm University, Department of Mathematics, Stockholm, S-10691, Sweden.
For a class of one-dimensional Schrödinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit distribution in the complex plane as the eigenvalues tend to infinity. This limit distribution depends only on the degree of the polynomial potential and on the boundary conditions.
Keywords: Eigenfunctions, PT-symmetry, Stokes phenomena, asymptotics.
MSC 2000: 34B05, 34L20, 34M40, 34M60.
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