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arXiv · 0711.3887

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

Omar Mustafa
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Abstract

A non-Hermitian P$_ϕ$T$_ϕ$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H$_{r}$, H$_θ$, and H$_ϕ$ 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$_ϕ$T$_ϕ$-symmetrized H$_ϕ$, 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 $V(θ)$=0 in the descendant Hamiltonian H$_θ$ would manifest a change in the angular $θ$-dependent part of the general solution too. Whilst some P$_ϕ$T$_ϕ$-symmetrized H$_ϕ$ 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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Omar Mustafa. 2008-01-24. Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry. https://doi.org/10.1007/s10773-008-9794-y

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