Geodesic
Invariant solution of the Dirac equation in the crossed electric and magnetic fields $(H > E)$
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 138-141.

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In the article exact analytical and invariant solutions for both spinless and half-spin relativistic charged particles in crossed constant electric and magnetic fields, when $H > E$ have been found. It is shown that in both cases the problem reduces to that of quantum harmonic oscillator.
Keywords: crossed electric and magnetic fields
Mots-clés : Invariant solution, Klein–Gordon equation, Dirac equation. 
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R. G. Petrosyan; М. А. Davtyan. Invariant solution of the Dirac equation in the crossed electric and magnetic fields $(H > E)$. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 138-141. http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a8/

[1] W. Gordon, “Der Comptoneffekt nach der Schrödingerschen Theorie”, Zeitschrift für Physik, 40:1–2 (2005), 117–133 | DOI | Zbl

[2] D. M. Wolkow, “Über eine Klasse von Lösungen der Diracschen Gleichung”, Z. Phys., 94:3–4 (1935), 250–260 | Zbl

[3] V. Canuto, C. Chiuderi, “Chiuderi Solution of the Dirac Equation in Orthogonal Electric and Magnetic Fields”, Lettere al Nuovo Cimento, 2:6 (1969–1970), 223–227

[4] L. Lam, “Dirac Electron in Orthogonal Electric and Magnetic Fields”, Lettere al Nuovo Cimento, 3:9 (1969–1970), 292–294

[5] V. B. Berestetskii, L. P. Pitaevskii, E. M. Lifshitz, Quantum Electrodynamics, v. 4, 2nd ed., Butterworth–Heinemann, 1982

[6] I. S. Gradshtein, I. M. Ryzhik, Tables of Integrals, Sums, Series and Products, Nauka, M., 1971, 1108 pp. (in Russian)

[7] L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, v. 2, Pergamon, Oxford, 1959