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The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. Atransition is implemented to a Schr\"odinger-type relativistic equation. Forthe case where the angular and radial variables are not separated, the methodof obtaining effective potentials is generalized. Effective potentials haveisolated singularities on the event horizons as well as at certain parametersof the Kerr-Newman field and of the fermion in the neighborhoods of some valuesof the radial coordinate. For the extreme Kerr-Newman field, the impossibilityof existence of stationary bound states of half-spin particles is proved.

Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations