Abstract
We obtain a new class of solutions of the Maxwell equations describing the spectrum of hydrogen. We prove that, instead of the quantum-mechanical Dirac equation, the ordinary classical Maxwell equations can be applied to the solution of many problems in atomic and nuclear physics.
Similar content being viewed by others
References
H. Sallhofer, “Elementary derivation of the Dirac equation. I,” Z Naturforsch. A., 33, 1379–1381 (1978)
H. Sallhofer, “Maxwell—Dirac—Isomorphism. XI.”, Z. Naturforsch. A. 41, 1087–1088 (1986).
H. Sallhofer, “Hydrogen in electrodynamics. II.,” Z. Naturforsch. A., 44, 167–168 (1989).
H. Sallhofer, “Hydrogen in electrodynamics. V,” Z. Naturforsch. A., 45, 1038–1040 (1990).
H. Sallhofer, “Hydrogen in electrodynamics. VI,” Z. Naturforsch. A., 45, 1361–1366 (1990).
A. Lakhtakia, Models and Modelers of Hydrogen, World Scientific, London (1996).
V. M. Simulik, “Connection between symmetry properties of the Dirac and Maxwell equations and conservation laws,” Teor. Mat. Fiz., 87, No. 4, 76–85 (1991).
I. Yu. Krivskii and V. M. Simulik, “Dirac equation and the representation of spin one, connection with symmetries of the Maxwell equations,” Teor. Mat. Fiz. 90, No. 3, 388–406 (1992).
V. M. Simulik, “Some algebraic properties of Maxwell-Dirac isomorphism,” Z. Naturforsch. A., 49, 1074–1076 (1994).
V. M. Simulik and I. Yu. Krivskii, “Complete collection of transformations connecting the Dirac and Maxwell equations,” Dopov. Akad. Nauk Ukr., No. 7, 54–57 (1995)
I. Yu. Krivskii and V. M. Simulik, “On the unitary operator connecting the Maxwell and Dirac equations,” Dopov. Akad. Nauk Ukr., No. 8. 79–85 (1996).
I. Yu. Krivsky and V. M. Simulik, “Unitary connection in Maxwell-Dirac isomorphism and the Clifford algebra,” Adv. Appl. Cliff Alg., 6, No. 2, 249–259 (1996).
V. M. Simulik and I. Yu Krivsky, “A classical electrodynamical model of the hydrogen atom,” in: Scientific Works of IÉF' 96, Uzhgorod (1996), pp. 27–31.
V. M. Simulik and I. Yu. Krivsky, “An electrodynmical version of the hydrogen spectrum,” in: Proceedings of the 28 th European Group of Atomic Spectroscopy Conf. (July, 1996), Graz., Austria (1996), pp. 41–42.
R. Mignani, E. Recami, and M. Baldo, “About a Dirac-like equation for the photon according to Ettore Majorana,” Lett. Nuovo Cim., 11, No. 12, 572–586 (1974).
I. Yu. Krivskii and V. M. Simulik, Foundations of Quantum Electrodynamics in Terms of Strengths [in Russian], Naukova Dumka, Kiev (1992).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).
M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions [Russian translation], Nauka, Moscow (1979).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum [in Russian], Nauka, Moscow (1975).
Additional information
Institute of Electron Physics, Ukrainian Academy of Sciences, Uzhgorod. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 958–969, July, 1997.
Rights and permissions
About this article
Cite this article
Simulik, V.M. Solutions of the Maxwell equations describing the spectrum of hydrogen. Ukr Math J 49, 1075–1088 (1997). https://doi.org/10.1007/BF02528753
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02528753