Geodesic
A new class of solutions of the Dirac equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 315-323

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A class of exact solutions of the Dirac equation is obtained for an electron in the electromagnetic field of a waveguide formed by two pairs of hyperbolic cylinders. The spin coefficients are determined in terms of the eigenvalues of the invariant polarization operator. The suggested method can be used to describe excitation in waveguides of arbitrary types. 
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     author = {Yu. G. Pavlenko and A. I. Toropova},
     title = {A new class of solutions of the {Dirac} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {120},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a10/}
}
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Yu. G. Pavlenko; A. I. Toropova. A new class of solutions of the Dirac equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 315-323. http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a10/