Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PTmathcal{PT}-symmetry |
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Authors: | Omar Mustafa and S. Habib Mazharimousavi |
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Affiliation: | (1) Department of Physics, Eastern Mediterranean University, G Magusa, North Cyprus, Mersin 10, Turkey |
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Abstract: | Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are 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 -symmetrized H φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-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 -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 -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric. |
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Keywords: | Non-Hermitian Hamiltonians Spherical-separability Pseudo- IEq8" > /content/8364333406t5044r/10773_2008_9794_Article_IEq8.gif" alt=" $mathcal{PT}$" align=" middle" border=" 0" > -symmetry |
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