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Proceedings of the Indian Academy of Sciences - Section A

Search for a density-based alternative quantum mechanics of many-electron systems

Bimalendu Deb

Published Aug 1, 1984• 1 citation
Publisher
DOI
10.1007/bf02840340

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A new theoretical concept of quantum mechanics is proposed. The leading role is assigned to the electron as a non-point particle with a volume density of charge and mass. Based on the Hamilton-Jacobi equation, a nonlinear differential equation describing the dynamics of the charged substance of an electron is proposed. This new fundamental equation is transformed into the Schrödinger equation, with the density of the material substance of the electron being proportional to the square of the wave function. Since an electron in the form of a "cloud" of matter can change its configuration in space, we can give a classical interpretation to the process of generating a photon with a frequency and energy corresponding to the principles of quantum mechanics. Interference, diffraction, and the non-relativistic concept of electron spin is discussed.
This study deals with the physical (not the mathematical) origin of the quantum conditions. The assumption of an absolute space together with the speed of 369.5 km/s of the sun leads to cycloidal or helical orbits of the electron around the proton. This kind of orbits is a previously unnoticed fact and not compatible with the model of a closed circular standing wave. It is the aim of this study to search for alternative models. The Alternating Field model (AFM) assumes the existence of alternating fields for both the proton and the electron. The Higgs-field provides the energy requirements. By Puthoff’s effect, adapted for the electrostatic field, the electron changes its Compton frequency according to its position in the field. The interference of the alternating fields of the proton and the electron causes beats that are integer multiples of the orbital frequencies when the electron moves on Bohr’s orbits. Important results of this study are: The electrostatic Schwarzschild-radius is exactly half the value of the classical electron radius. Bohr’s first three principal quantum numbers, 1, 2, 3, are reproduced as 1.000052, 2.000214, and 3.000685. A two-dimensional simulation shows that the AFM causes orbits with ribbon shape. A formula, using only the orbital frequencies of the two innermost circular orbits, can predict the shortest wavelength of the Lyman series. The AFM is still incomplete. E.g., it does not prevent illegal orbits, but only indicates them. Also, the AFM does not use the magnetic core field of the proton. On the other hand, the model has produced results showing that Newton’s absolute space and the QM are compatible.
An alternative method of deriving the values of the observables of atomic systems is presented. Rather than using operators and eigenvalues the local variables method uses the continuity equation together with current densities derived from wave functions that are solutions of the Dirac or Pauli equation. The method is applied to atomic hydrogen using the usual language of quantum mechanics rather than that of geometric algebra with which the method is often associated. The picture of the atom that emerges is one in which the electron density as a whole is rotating about a central axis. The results challenge some assumptions of conventional quantum mechanics. Electron spin is shown to be a property of the dynamical motion of the electron and not an intrinsic property of the electron, the ground state of hydrogen is shown to have an orbital angular momentum of ℏ, and excited states are shown to have angular momenta that are different from the eigenvalues of the usual quantum mechanical operators. The uncertainty relations are found not to be applicable to the orthogonal components of the angular momentum. No double electron spin gyromagnetic ratio is required to account for the observed magnetic moments, and the behavior of the atom in a magnetic field is described entirely in kinetic terms.