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Results in Physics

Particles and quantum waves diffusion in physical vacuum

Arvydas Juozapas Janavičius

Published Jul 20, 2018• 0 citations
Publisher

Abstract

The new quantum waves’ diffusion equation based on Heisenberg uncertainties and De Broglie’s frequencies of waves is presented. The free movement and quantum diffusion through a rectangular barrier are considered. We find a quantum diffusion coefficient and radii of bound systems. The obtained formula connecting radii and bound energies of simple quantum systems, such as a hydrogen atom, deuteron and mesons, consisted of quarks.

DOI
10.1016/j.rinp.2018.07.020

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The new quantum waves’ diffusion equation based on Heisenberg uncertainties and De Broglie’s frequencies of waves is presented. The free movement and quantum diffusion through a rectangular barrier are considered. We find a quantum diffusion coefficient and radii of bound systems. The obtained formula connecting radii and bound energies of simple quantum systems, such as a hydrogen atom, deuteron and mesons, consisted of quarks.
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Schrödinger's equation can be considered as a diffusion equation with a diffusion coefficient β2=ℏ/2m. In this article, we explore the implications of this view. Rewriting the wave function in a polar form and transforming Schrödinger's equation into two real equations, we show that one of them reduces to the continuity equation, and the other, a nonlinear dynamical equation for the probability density. Considering these two equations as if they were the basic equations of quantum mechanics, we apply them to several one-dimensional quantum systems. We show the dispersive properties in the probability densities of stationary states of a particle in a rigid box and in harmonic potential; quasi-classical Gaussian probability densities of a free particle; and coherent states and squeezed states of the harmonic oscillator. We also present the soliton as a quantum mechanical representation of a free particle. We discuss the meaning of the diffusion coefficient β2 for each quantum system using a density plot.
It is shown that, with suitable conventions, Schrödinger's equation can be deduced from the lows of stochastic diffusion: uncertainty relations, concrete meaning of mass-energy equivalence, minimal constants of time and length and vanishing of negative energy also appear resulting from the basic conventions. An extension to mechanics with spin is worked out, and a model of Dirac's fluied is elaborated. Stochastic assumptions also lead to the energy states and quantum numbers of the hydrogen atom. Suggestions are made on the physical interpretation of the model, on its relation to the wave-particle dualism, and on the meaning of quantized states.
In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in classical mechanics. In order to illustrate the fundamental differences between the two theories, one of the simplest problems of particle dynamics is solved in both Newtonian and quantum mechanics. This simple example also helps to show that quantum mechanics is the fundamental theory and classical mechanics is an approximation, a remarkably good approximation, when considering macroscopic objects. The solution of the Schrödinger equation is presented for a particle inside a box and the quantization condition is derived. The amazing possibility of quantum tunneling when a particle is incident on a barrier of height larger than the energy of the incident particle is also discussed. Finally the three-dimensional Schrödinger equation is solved for the hydrogen atom.
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 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.