Finite-Dimensional PT-Symmetric Hamiltonians

Details Finite-Dimensional PT-Symmetric Hamiltonians Finite-Dimensional PT-Symmetric Hamiltonians

2003-03-29

arxiv.org/abs/quant-ph/0303174v1

Physics

Quantum Physics

8 pages, 1 figure

Scientific paper

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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