 02319 K. C. Shin
 The potential $(iz)^m$ generates real eigenvalues only, under symmetric rapid decay conditions
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Jul 22, 02

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Abstract. We consider the eigenvalue problems
$u"(z)\pm (iz)^m u(z)=\lambda u(z)$, $m\geq 3$,
under every rapid decay boundary condition that is symmetric
with respect to the imaginary axis in the complex $z$plane.
We prove that the eigenvalues $\lambda$ are all positive real.
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