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arXiv · quant-ph/0303174

Finite-Dimensional PT-Symmetric Hamiltonians

Carl M. Bender·Peter N. Meisinger·Qinghai Wang
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Abstract

This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.

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Carl M. Bender, Peter N. Meisinger, Qinghai Wang. 2003-03-29. Finite-Dimensional PT-Symmetric Hamiltonians. https://doi.org/10.1088/0305-4470%2F36%2F24%2F314

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