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Who Needs Wave Equations

Jean Louis Van Belle

Published Dec 1, 2018• 0 citations
OpenAlex

Abstract

This paper further explores a dual interpretation of the Uncertainty Principle as applied to the classical Rutherford-Bohr calculations of the geometry of the hydrogen electron orbitals. It shows the Rutherford-Bohr model has some advantages over the quantum-mechanical model (Schrodinger’s equation for the hydrogen atom). As such, it basically continues a development started in my previous paper (http://vixra.org/abs/1812.0028). What is novel in this paper is the exploration of the mathematical equivalence between both models.

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This paper further explores a dual interpretation of the Uncertainty Principle as applied to the classical Rutherford-Bohr calculations of the geometry of the hydrogen electron orbitals. It shows the Rutherford-Bohr model has some advantages over the quantum-mechanical model (Schrodinger’s equation for the hydrogen atom). As such, it basically continues a development started in my previous paper (http://vixra.org/abs/1812.0028). What is novel in this paper is the exploration of the mathematical equivalence between both models.
Through his experiments, the physicist Niels Bohr improved upon Rutherford's model of the atom and developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of the hydrogen atom. A simple means for extending the conventional non-relativistic Bohr model of the atom to include the wave nature of electrons is presented. As the derivation requires basic knowledge of classical and wave mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics.
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
The new quantum theory was a mathematical description of the way in which an electron behaves when bounded by some kind of potential – such as being in an electric field, acting as a harmonic oscillator or simply being confined to a certain area of space. This mathematical description was then interpreted to be a description of the electron as being probabilistic. It was Schrödinger’s wave equation, together with de Broglie’s concept of a matter wave, that led to various important concepts like the Heisenberg uncertainty principle, an explanation of the emission and absorption of photons in atoms, quantum tunnelling and so on. This chapter explains what Schrödinger did – the marriage of waves and particles.
The Bohr model is historically important in the understanding of quantum physics. It gives many important results for the hydrogen atom including atomic size and ionization energy. It is sometimes referred to as a semi-classical calculation, because it includes the physics of angular momentum quantization without the full quantum mechanical description of an electron wave. It is tremendously useful for gaining physical intuition of the quantum nature of the atom. In the Bohr model of the hydrogen atom, an electron has a circular orbit with speed v and radius r about the proton. The Bohr quantization condition is that an integer number of electron (de Broglie) wavelengths must fit to the atomic circumference.