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

Blank J

Dieudonné J

Reed M

von Neumann J

English

arXiv

Ali Mostafazadeh

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Pseudo–Hermitian quantum mechanics with unbounded metric operators

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(+)

Mostafazadeh, Ali

Koç University Digital Collections

Pseudo-Hermitian quantum mechanics with unbounded metric operators

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(+).Turkish Academy of Sciences (TUBA

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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators


            I extend the formulation of pseudo-Hermitian quantum mechanics to
            η
            +
            -pseudo-Hermitian Hamiltonian operators
            H
            with an unbounded metric operator
            η
            +
            . 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
            η
            +
            and consequently
            
              
            
            .
          </jats:p

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Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators

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