Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT}
-symmetry |
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Authors: | Omar Mustafa and S Habib Mazharimousavi |
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Institution: | (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- " target="_blank">gif" alt="$\mathcal{PT}$" align="middle" border="0"> -symmetry |
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