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

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

2006-01-18

arxiv.org/abs/quant-ph/0601123v1

J.Phys.A39:1945-1953,2006

Physics

Quantum Physics

10 pages, 2 figures

Scientific paper

10.1088/0305-4470/39/8/011

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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