Summary
As a consequence of the theory of the characteristics of the partial differential equations the law of motion of the wave front of a quantal wave moving in electrostatic and magnetostatic fields is formally identical with the corresponding law for zero magnetic fields. And phase velocity, wavelength, and refractive index are formally identical both in the presence and in the absence of magnetic fields.
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References
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Loinger, A. On the phase velocity of the quantal waves. Nuov Cim A 108, 1115–1123 (1995). https://doi.org/10.1007/BF02790319
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DOI: https://doi.org/10.1007/BF02790319