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arXiv · 0807.0424

Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra

Carl M Bender·Daniel W Hook·Lawrence R Mead
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Abstract

The spectrum of the Hermitian Hamiltonian $H=p^2+V(x)$ is real and discrete if the potential $V(x)\to\infty$ as $x\to\pm\infty$. However, if $V(x)$ is complex and PT-symmetric, it is conjectured that, except in rare special cases, $V(x)$ must be analytic in order to have a real spectrum. This conjecture is demonstrated by using the potential $V(x)=(ix)^a|x|^b$, where $a,b$ are real.

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Carl M Bender, Daniel W Hook, Lawrence R Mead. 2008-07-03. Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra. https://doi.org/10.1088/1751-8113/41/39/392005

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