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Elsevier eBooks

Operator Method in Quantum Mechanics

Published Jan 1, 1981• 4 citations
Publisher
DOI
10.1016/b978-0-444-00410-9.x5001-x

Related papers

Exponential operator methods for solving partial differential equations in quantum mechanics

Hai Shen

•Jan 1, 1991•0 citations

Exploring and analysis on the operational question of operator

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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.

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Operator Methods in Quantuin Mechanics

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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.

•Nov 28, 1991•61 citations

The Operators of Quantum Mechanics

Philip Franklin

Studies in Applied Mathematics•Apr 1, 1929•1 citation

Operator Ordering in Quantization on the Sphere

Masayoshi Nakamura, Hiroaki Minowa, Nobuhiko Mishima

The problem of the quantization of an elementary model with the second class constraints, O(n) rigid rotator model, is investigated by using the Dirac method, the projection operator method (POM) and the nonlinear quantum mechanics (NLQM). It is proved that the quantum effects, which are equivalent to those of NLQM, appear in the equation of motion of POM. Furthermore, it is shown that POM as well as NLQM preserves the isometric symmetry, which the system possesses in the classical level, through the quantization process.

Progress of Theoretical Physics•Jan 1, 1988•2 citations
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.
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 problem of the quantization of an elementary model with the second class constraints, O(n) rigid rotator model, is investigated by using the Dirac method, the projection operator method (POM) and the nonlinear quantum mechanics (NLQM). It is proved that the quantum effects, which are equivalent to those of NLQM, appear in the equation of motion of POM. Furthermore, it is shown that POM as well as NLQM preserves the isometric symmetry, which the system possesses in the classical level, through the quantization process.