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Dirac's equation in the field of a circularly polarized electromagnetic waveand constant magnetic field has exact localized non-stationary solutions. Thesolutions corresponds relativistic fermions only. Among them singular solutionswith energy eigenvalues close to each other are found. The solutions are mostpracticable and can be separated by means of the phase matching between themomentum of the electromagnetic wave and spinor. Characteristic parameters ofthe singular states are defined.

Singular states of relativistic fermions in the field of a circularly polarized electromagnetic wave and constant magnetic field