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.