Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry

Abstract

A non-Hermitian P${}_{\varphi }$T${}_{\varphi }$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H${}_r$, H${}_{\theta }$, and H${}_{\varphi }$ play essential roles and offer some user-feriendly options as to which one (or ones) of them is (or are) non-Hermitian. Considering a P${}_{\varphi }$T${}_{\varphi }$-symmetrized H${}_{\varphi }$, we have shown that the conventional relativistic energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction $V(\theta )$=0 in the descendant Hamiltonian H${}_{\theta }$ would manifest a change in the angular $\theta$-dependent part of the general solution too. Whilst some P${}_{\varphi }$T${}_{\varphi }$-symmetrized H${}_{\varphi }$ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the PT-symmetric ones (here the non-Hermitian

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References in corpus (5)

• Dirac equation exact solutions for generalized asymmetrical Hartmann potentials
• Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $\eta$-pseudo-Hermiticity generators
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Non-Hermitian Hamiltonian versus E=0 localized states
• PT-symmetry, ghosts, supersymmetry and Klein-Gordon equation