PT Symmetry as a Generalization of Hermiticity

Abstract

The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the PT-symmetric Hamiltonian represents the most general matrix Hamiltonian with a real spectrum. In both cases, Hermitian matrices are shown to be special cases of PT-symmetric matrices. This finding confirms and strengthens the early belief that the PT-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics.

13 pages

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems

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