An alternative construction of the positive inner product in non-Hermitian quantum mechanics

Details An alternative construction of the positive inner product in non-Hermitian quantum mechanics An alternative construction of the positive inner product in non-Hermitian quantum mechanics

2009-05-10

arxiv.org/abs/0905.1454v2

Physics

Quantum Physics

11 pages, some minor typos fixed, to appear in Physics Letters B

Scientific paper

Within the context of non-Hermitian quantum mechanics, we use the generators of eigenvectors of the Hamiltonian to construct a unitary inner product space. Such models have been of interest in recent years, for instance, in the context of ${\cal PT}$ symmetry, although our construction extends to the larger class of so-called pseudo-Hermitian Operators. We provide a detailed example to illustrate the concept and compare with known results.

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