Finite-Dimensional PT-Symmetric Hamiltonians

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.

8 pages, 1 figure

References in corpus (4)

• Quantum Entanglement of Moving Bodies
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• All Hermitian Hamiltonians Have Parity
• P,T,PT, and CPT invariance of Hermitian Hamiltonians

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• Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum Theory?
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