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Journal of Zunyi Normal College

Concluding and Proving the Commutation Relation of Operators often Used in Quantum Mechanics

Wan Meng

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In order to help physical students really understanding the commutation relation of operators,we analyze,conclude and summarize the commutation relations of operators often used in quantum mechanics,which provide some references for teaching of quantum mechanics course as well.

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Leaves from the angle of teaching research,the problems of quantum mechanics in quantization concept and application commutation relations of generation operators in certain a quantity of mechanical representation for the simplify calculation for commutation relations of generation operators and spread out coefficient for principle of superposition taking number in the field of complex number and significance of physics and number occupation representation have analysed and discussed, have clarified some misunderstandings, have deepened knowledge and the understanding for some concept and method.
Abstract Quantum mechanical problems capable of exact solution are traditionally solved in a few instances only (such as the harmonic oscillator and angular momentum) by operator methods, but mainly by means of Schrodinger's wave mechanics. The present volume shows that a large range of one- and three-dimensional problems, including certain relativistic ones, are solvable by algebraic, representation-independent methods using commutation relations, shift operators, the virial, hypervirial, and Hellman-Feyman theorems. Applications of these operator methods to the calculation of eigenvalues, matrix elements, and wavefunctions are discussed in detail. This book is an introduction to the use of operator methods in quantum mechanics and also a reference work with numerous problmes solved. It is suitable for use by students of intermediate quantum mechanics and also more advanced postgraduate students who wish to study the algebraic method of solving quantum mechanical problems.
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the operator formalisms are generally given theoretically and it is documented that these abstract formalisms are usually misunderstood by the students. Based on the idea that quantum mechanical phenomena can be investigated via geometric optical tools, this study aims to introduce an experiment, where the quantum mechanical commutation relations are represented in a concrete way to provide students an easy and permanent learning. The experimental tools are chosen to be easily accessible and economic. The experiment introduced in this paper can be done with students or used as a demonstrative experiment in laboratory based or theory based courses requiring quantum physics content; particularly in physics, physics education and science education programs.