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Soviet physics. Doklady

AN ALGORITHM OF QUANTUM MECHANICS

I. S. Arzhanykh

Published May 1, 1959• 0 citations
OpenAlex

Abstract

An attempt was made to develop a universal algorithm which in one realization describes the equations of classical mechanics and in another realization the equations of quantum mechanics. Hence, a synthesis can be derived as the difference and the relation between the first and sccond realizations. (R.V.J.)

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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)].
This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum while ignoring the angular momentum, spin or other particle characteristics. The main result of the paper shows that the colliding two particle classical Hamiltonian energy can be represented in four weighted individual particle in symmetric and anti-symmetric (osmotic) terms similar to the quadratic Nelson measure used in the derivation of the Schrodinger wave function. Following Nelson, if the second particle behavior can be captured in a potential and the ingoing and outgoing velocities of the main particle are modelled using stochastic differential equations the motion of the main particle satisfies the Schrodinger's equation. The diffusion variance of this equation is replaced by a related ratio of masses and the assumed variance. The first example attempts to reconcile this result with quantum mechanics by considering the Schrodinger equation in the presence of only one type of incident particle. The main particle energy levels become multiples of the incident particle and the energy expression for the entire system agrees with quantum mechanics but there are differences with the stochastic equation. The Schrodinger equation can also be used to represent corrections for Newton's equation and suggests a user profile to be used in the search for Dark Matter. An alternative solution to the collision model also shows relativistic properties as the interactions suggest corrections to the Minkowski equation in Einstein's Special Relativity. It is also possible to use the classical Schrodinger's equation both on the main and incident particle simultaneously leading to a correlated set of wave equations with different diffusion parameters.