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Journal of Anyang Normal University

On Some Kinds of Operator Operation Methods in Quantum Mechanics

Dai Yan-wei

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

This text is through introducing the daily operation method of several kinds of operators for example: Direct method , function method , parameter differentiation method, integral transformations method , undetermined operator method , representation method.

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In the quantum mechanics,the whole characteristic can be reflected well using the operator.Meanwhile,the mechanical properties can be distilled from the wave function by the operator.When solving or inferring the relation of operators,we not only grasp the significance and property of the related operator,but also understand some basic operational methods of operator.This paper introduces several common operational methods of operator in the quantum mechanics through giving examples.Such as the direct,functional,parameter differential,undetermined operator,integral transform, mathematical induction methods and so on.
In this paper we propose a new method of nonlinear transformation(Eigen-Mapping) to treat the eigenvalue problems in quantum mechanics as examples.The basic idea is to make the matrix of some operator we concerned diagonalization through introduction of small undetermined parameters and establishment equations for matrix elements.These problems can be devided into two types based on that there are or not 1st order approximate solution for them(in sense of the perturbation theory).In either type we consider also two cases of degenerate and nondegenerate.To obtain solution or approximate solution for eigenvalue problems,it is given the procedures of the method and usable formulas exhaustively.Seven examples in this paper are a common sight in general course of quantum mechanics.The results from them are compared with that from other approximate methods(for examples: perturbation method and variation method).After checking the results obtained,we can see that this new method has many advantages.