Classical-field model of the hydrogen atom

Abstract

It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field, an "electron wave", which is held in a limited region of space by the electrostatic field of the proton. It is shown that quantum mechanics must be considered to be not a theory of particles but a classical field theory in the spirit of classical electrodynamics. In this case, we are not faced with difficulties in interpreting the results of the theory. In the framework of classical electrodynamics, all of the well-known regularities of the spontaneous emission of the hydrogen atom are obtained, which is usually derived in the framework of quantum electrodynamics. It is shown that there are no discrete states and discrete energy levels of the atom: the energy of the atom and its states change continuously. An explanation of the conventional corpuscular-statistical interpretation of atomic phenomena is given. It is shown that this explanation is only a misinterpretation of continuous deterministic processes. In the framework of classical electrodynamics, the nonlinear Schrödinger equation is obtained, which accounts for the inverse action of self-electromagnetic radiation of the electron wave and completely describes the spontaneous emissions of an atom.

Nonlinear Schrödinger equation and semiclassical description of the microwave-to-optical frequency conversion based on the Lamb–Retherford experiment

“…At the same time, it was shown in [8][9][10][11] that all the basic properties of the hydrogen atom can be easily explained within the framework of classical field theory if the electron is considered not as a particle which has the properties unusual from the classical point of view but as an This point of view fully agrees with the classical concepts of fields and particles and does not require the postulating of any special "quantum", nonclassical properties of the electromagnetic field and the "electron" [8][9][10][11][12][13][14].…”

“…In particular, as shown in [9], from this point of view, the hydrogen atom can be regarded as a classical open volume resonator in which the electron wave is held due to "total internal reflection", while the Coulomb field of the proton plays the role of the dielectric medium. The electron wave in a hydrogen atom is a completely classical continuous (not quantized) field, analogous to a classical electromagnetic field, and does not reduce to any particles or quanta.…”

“…Within the framework of the theory [8][9][10][11], there are no problems with the explanation of the spontaneous transition, which is a trivial consequence of classical electrodynamics, as a result of the inverse action of the self-radiation field on atom. The taking into account the self-radiation field leads to the appearance of nonlinear terms in the Schrodinger equation, which describe the change in the structure of the hydrogen atom in the process of spontaneous emission [9].…”

Thermostatistics of classical fields

“…For the "quanta" of the classical "bosonic" field which is in equilibrium with the thermal reservoir, the Bose-Einstein statistics are obtained in a natural way, while for the "fermionic" field which is in equilibrium with the thermal reservoir, the statistics close to the Fermi-Dirac and Gentile statistics was obtained. This indicates that many of the results of quantum statistics can apparently be obtained within the framework of classical field theory, when the electromagnetic field and the electronic field are considered as the classical fields [1][2][3].…”

Generalized Fock space and contextuality

“…The common opinion that such a representation does not exist was originally based on the straightforward interpretation of the Heisenberg's uncertainty principle, negativity of the Wigner distribution, and later by various no-go theorems, e.g., the von Neumann, Kochen-Specker, and Bell theorems. However, the real situation is more complicated, see, e.g., Man'ko et al [13][14][15][16], Khrennikov et al [6][7][8][17][18][19], and Dzhafarov et al [20][21][22][23][24][25] See especially their recent works [13,25,19,26]; see also papers on the attempts to reproduce quantum probabilities and correlations by using theory of classical random fields [27][28][29][30][31][32][33][34][35].…”