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Calculation of the Hidden Symmetry Operator for a $\cP\cT$-Symmetric Square Well

Carl M. Bender·Barnabas Tan
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Abstract

It has been shown that a Hamiltonian with an unbroken $\cP\cT$ symmetry also possesses a hidden symmetry that is represented by the linear operator $\cC$. This symmetry operator $\cC$ guarantees that the Hamiltonian acts on a Hilbert space with an inner product that is both positive definite and conserved in time, thereby ensuring that the Hamiltonian can be used to define a unitary theory of quantum mechanics. In this paper it is shown how to construct the operator $\cC$ for the $\cP\cT$-symmetric square well using perturbative techniques.

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Carl M. Bender, Barnabas Tan. 2006-01-18. Calculation of the Hidden Symmetry Operator for a $\cP\cT$-Symmetric Square Well. https://doi.org/10.1088/0305-4470/39/8/011

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