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Chinese journal of atomic and molecular physics

The description with double-wave function for particle in single-atom model potential

Gang Chen

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

The description with double-wave function for particle in single-atom model potential is obtained by using the quantum theory of double-wave function. It is indicated that the double-wave function describes the kinematical law of single particle. This description involves the general quantum mechanics result in statistical average of system.

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The description with double-wave function for particle in single-atom model potential is obtained by using the quantum theory of double-wave function. It is indicated that the double-wave function describes the kinematical law of single particle. This description involves the general quantum mechanics result in statistical average of system.
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.
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.