Nonunique C operator in PT Quantum Mechanics

Details Nonunique C operator in PT Quantum Mechanics Nonunique C operator in PT Quantum Mechanics

2009-05-28

arxiv.org/abs/0905.4673v1

Phys.Lett.A373:2670-2674,2009

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, 1 figure

Scientific paper

10.1016/j.physleta.2009.05.066

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 $H={1/2}p^2+{1/2}\mu^2q^2+i\epsilon q^3$ is determined perturbatively to first order in $\epsilon$ 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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