Pseudo-Hermitian quantum mechanics with unbounded metric operators

Abstract

I extend the formulation of pseudo-Hermitian quantum mechanics to eta(+)-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta(+). In particular, I 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 root eta(+).