02-319 K. C. Shin
The potential $(iz)^m$ generates real eigenvalues only, under symmetric rapid decay conditions (76K, LaTex2e with 1 eps figure) 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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