Pseudo-Hermiticity versus PT Symmetry: The structure responsible for the reality of the spectrum of a non-Hermitian Hamiltonian

نویسنده

  • Ali Mostafazadeh
چکیده

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT -symmetric non-Hermitian Hamiltonians studied in the literature are pseudo-Hermitian and argue that the structure responsible for the reality of the spectrum of these Hamiltonian is their pseudo-Hermiticity not PT -symmetry. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudo-supersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRWmodels coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.

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تاریخ انتشار 2001