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Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms

Quantum Wave Equation for Non-conservative System

Yi-Qing Guo

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

It is well known that the Schrdinger equation is only suited for the particle which lies in a conservative force field.In atomic physics and molecular physics,a particle may suffer the action of non-conservative forces.In this paper,a new quantum wave equation was proposed,which can describe the particle lying in a non-conservative field.The new quantum wave equation can be used in some research fields.

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It is well known that the Schrdinger equation is only suited for the particle which lies in a conservative force field.In atomic physics and molecular physics,a particle may suffer the action of non-conservative forces.In this paper,a new quantum wave equation was proposed,which can describe the particle lying in a non-conservative field.The new quantum wave equation can be used in some research fields.
In this work a new representation of quantum mechanics, that is, the electromagnetic field representation, is proposed, which is different from the Schr dinger`s equation and Heisenberg`s Matrix. It is pointed out that even though the results from Schr dinger`s equation, Heisenberg`s Matrix and electromagnetic field representation in describing the quantum system are the same, the principles and procedures in describing the quantum system are totally different. The further result regarding the application of the electromagnetic field representation of quantum mechanics to different atomic and molecular systems will be presented later.
The Schr?dinger differential equation is what we usually solve for the microscopic particles in non-relativistic quantum mechanics. Niels Bohr suggested the power two of the (usually) complex answer shows the probability of the particle’s existence at a point of space. Also, the time dependence of Schrodinger wave equation is one whereas for light in electromagnetism is two. In this paper, we show a solution for both problems. We derive a Wave Equation for the energy of every system. This electromagnetic wave equation is shown to convert to those classical (i.e. the Schrodinger) and special relativistic (i.e. Klein-Gordon) quantum mechanical equations. Also, accordingly there definitely is a physical meaning to answer to this wave equation. And therefore, switching the probabilistic interpretation of quantum mechanics to a deterministic one as (Albert) Einstein demanded.
Two types of Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time-dependent one and an alternative class of nonlinear Hamiltonians. In the latter group we propose a new form. By Ehrenfest’s theorem the expectation values of the operators of physical observables correspond to the classical quantities. For all Schrödinger equations we derive and discuss wavepacket, wave, stationary, and pseudostationary solutions of force free motion, free fall, and harmonic oscillator.