Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators

Abstract

We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space, observables, and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of eta and consequently its positive square root.

8 pages, accepted for publication in Phil. Trans. R. Soc. A

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators

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