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arXiv · 0905.4673

Nonunique C operator in PT Quantum Mechanics

Carl M. Bender·S. P. Klevansky
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Abstract

The three simultaneous algebraic equations, $C^2=1$, $[C,PT]=0$, $[C,H]=0$, which determine the $C$ operator for a non-Hermitian $PT$-symmetric Hamiltonian $H$, are shown to have a nonunique solution. Specifically, the $C$ operator for the Hamiltonian $H={1/2}p^2+{1/2}μ^2q^2+iεq^3$ is determined perturbatively to first order in $ε$ and it is demonstrated that the $C$ operator contains an infinite number of arbitrary parameters. For each different $C$ operator, the corresponding equivalent isospectral Dirac-Hermitian Hamiltonian $h$ is calculated.

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Carl M. Bender, S. P. Klevansky. 2009-05-28. Nonunique C operator in PT Quantum Mechanics. https://doi.org/10.1016/j.physleta.2009.05.066

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