  Non-Hermitian but P(phi)T(phi)-symmetrized spherically-separable Dirac and
Schrodinger Hamiltonians are considered. It is observed that the descendant
Hamiltonians H(r), H(theta), and H(phi) 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(phi)T(phi)-symmetrized H(phi), we have shown
that the conventional Dirac (relativistic) and Schrodinger (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(theta) in the descendant Hamiltonian H(theta) would
manifest a change in the angular theta-dependent part of the general solution
too. Whilst some P(phi)T(phi)-symmetrized H(phi) 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 P(phi)T(phi)-symmetric
Hamiltonians) are nicknamed as pseudo-PT-symmetric.

Quantum Physics