Abstract
The mechanism of introducing non-Hermiticity to non-central -symmetric potentials through both the φ azimuth and θ polar angles is discussed. Generalizing the results of a previous work it is shown that this can be done also through the polar angle part if appropriate potentials, such as the Scarf I or Rosen–Morse I potentials are used in the eigenvalue equation of the polar component. It is shown that the spontaneous breakdown of symmetry can also occur in these non-central potentials. Several potentials are proposed in the azimuthal eigenvalue equation too, where the use of periodic boundary conditions is essential. Possible generalizations of the results are outlined.
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