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Acta Physica Sinica

DOUBLE-WAVE DESCRIPTION OF A TWO-DIMENSIONAL HYDROGEN ATOM

C Huang

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

Double wave quantum theory is applied to the description of a two dimensional hydrogen atom.The classical limit of this description is discussed.The results indicate that double wave function can be applied to describe the states of single particle,and the ordinary quantum mechanical description,as a statistical average of ensemble,is included in the double wave quantum theory.

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arXiv:physics/0405117•May 21, 2004•5 citations
Double wave quantum theory is applied to the description of a two dimensional hydrogen atom.The classical limit of this description is discussed.The results indicate that double wave function can be applied to describe the states of single particle,and the ordinary quantum mechanical description,as a statistical average of ensemble,is included in the double wave quantum theory.
In this paper, double-wave quantum theory is applied to describe a thr ee-dimensional hydrogen atom and a three-dimensional similar hydrogen atom, the classical limit of this description is discussed. It is proved that double-wave function satisfies the normalization condition. Under the description of double- wav e functions, the expectation value of energy and angular momentum are E n a nd m, respectively. A t the same time, we calculated the average values of r, cos θ, sin θ , cos φ, sin φ and X, Y, Z, under the description of double-wave fu nction. The statistical average va lue for mechanics quantity  shows that single-wave function describes the states of the system of hydrogen atom and similar hydrogen atom. Only double-wave func tion can describe the states of single microcosmic body.
Double wave quantum theory is applied to describe the motion of charged particle in a uniform magnetic field. This description of the motion of the particle is complete. One can tell the value of an arbitrary physical quantity at any time. The probability and the formula to calculate mean values in ordinary quantum mechanics comes from the average of double wave description over a certain ensemble. The rule of gauge transformation in quantum mechanics can be seen from the average over an ensemble.
It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.