Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Kashgar Teachers College

Four Notes on the Quantum Mechanics

Yunhu Wu

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Wan Meng

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.

Journal of Zunyi Normal College•Jan 1, 2011•0 citations

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Anthony J. Bracken

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

•Apr 14, 2005•5 citations

Operator Methods in Quantuin Mechanics

Owen L. de Lange, R. E. Raab

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

Quantum Mechanical Operators

Ram Yatan Prasad, Pranita

In the present chapter, before discussing the mechanical operators, operator has been lucidly defined and examples are cited for its clear understanding. It includes linear and non-linear operator, commutator and commutation, and Hermitian operator and its properties. It also consists of Schmidt orthogonalisation, del and del 2 operators, linear momentum operator and it applications, angular momentum vector and commutation, and angular momentum in spherical polar co-ordinates. This chapter also provides a good discussion regarding ladder operator, Hamiltonian operator and its commutation, and relation of angular momentum operators with Hamiltonian operators. It also discusses projection operator clearly and solution of problem related to projection operator. The properties of projection operator have also been given. Suitable references have also been provided for the consultation. A large number of problems and their solutions relating to different operators have also been cited. Questions on concepts have also been provided for exercise purposes. The readers are advised to solve these problems for better understanding.

CRC Press eBooks•Jan 15, 2021•0 citations

Introduction

Jan Dereziński, Christian Gérard

Quantum fields and quantization are concepts that come from quantum physics, the most intriguing physical theory developed in the twentieth century. In our work we would like to describe in a coherent and comprehensive way basic aspects of their mathematical structure. Most of our work is devoted to the simplest kinds of quantum fields and of quantization. We will mostly discuss mathematical aspects of free quantum fields. We will consider the quantization only on linear phase spaces. The reader will see that even within such a restricted scope the subject is rich, involves many concepts and has important applications, both to quantum theory and to pure mathematics. A distinguished role in our work will be played by representations of the canonical commutation and anti-commutation relations . Let us briefly discuss the origin and the meaning of these concepts.

Cambridge University Press eBooks•Mar 6, 2013•0 citations

On students' misunderstanding of the basic concepts of Quantum Mechanics: case of Algerian Universities

Rabah Ladj, Mustapha Oldache, Chams-Eddine Khiari +1 more

Through many years of teaching Quantum Mechanics in Algerian universities, we have noticed that students face great obstacles in understanding the meaning of the basic concepts of this theory, such as the Wave Function, the Uncertainly Principle, the Superposition Principle and the Complementarity Principle. We believe that these obstacles rise due to the influence of basic concepts in Classical Mechanics which students studied for many years before studying Quantum Mechanics. For example, in Classical Mechanics, the concept of wave and the concept of corpuscle refer to different things, while in Quantum Mechanics both concepts refer to the same thing, namely a "quantum particle". In order to study the problem, a questionnaire sheet was presented to concerned students third-year (undergraduate physics students) before they studied the subject and after studying it. We note that these third-year students had had, as an introduction, a deep discussion of the meaning of quantum mechanical concepts for about one hour and a half a week during one month. To compare the results and show the importance of the epistemological and educational aspects, we presented again the same questionnaire to fifth-year physics students (B.Sc degree). We mention that the latter learned Quantum Mechanics without an epistemological introduction of the basic quantum mechanical concepts. Before giving our epistemological and didactical analysis of the results, we give a brief review of a previous didactical study related to the subject made by other authors. We conclude by giving some suggestions which we think are necessary in teaching Quantum Mechanics.

Latin American journal of physics education•Jan 1, 2010•1 citation
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.
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.
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.
In the present chapter, before discussing the mechanical operators, operator has been lucidly defined and examples are cited for its clear understanding. It includes linear and non-linear operator, commutator and commutation, and Hermitian operator and its properties. It also consists of Schmidt orthogonalisation, del and del 2 operators, linear momentum operator and it applications, angular momentum vector and commutation, and angular momentum in spherical polar co-ordinates. This chapter also provides a good discussion regarding ladder operator, Hamiltonian operator and its commutation, and relation of angular momentum operators with Hamiltonian operators. It also discusses projection operator clearly and solution of problem related to projection operator. The properties of projection operator have also been given. Suitable references have also been provided for the consultation. A large number of problems and their solutions relating to different operators have also been cited. Questions on concepts have also been provided for exercise purposes. The readers are advised to solve these problems for better understanding.
Quantum fields and quantization are concepts that come from quantum physics, the most intriguing physical theory developed in the twentieth century. In our work we would like to describe in a coherent and comprehensive way basic aspects of their mathematical structure. Most of our work is devoted to the simplest kinds of quantum fields and of quantization. We will mostly discuss mathematical aspects of free quantum fields. We will consider the quantization only on linear phase spaces. The reader will see that even within such a restricted scope the subject is rich, involves many concepts and has important applications, both to quantum theory and to pure mathematics. A distinguished role in our work will be played by representations of the canonical commutation and anti-commutation relations . Let us briefly discuss the origin and the meaning of these concepts.
Through many years of teaching Quantum Mechanics in Algerian universities, we have noticed that students face great obstacles in understanding the meaning of the basic concepts of this theory, such as the Wave Function, the Uncertainly Principle, the Superposition Principle and the Complementarity Principle. We believe that these obstacles rise due to the influence of basic concepts in Classical Mechanics which students studied for many years before studying Quantum Mechanics. For example, in Classical Mechanics, the concept of wave and the concept of corpuscle refer to different things, while in Quantum Mechanics both concepts refer to the same thing, namely a "quantum particle". In order to study the problem, a questionnaire sheet was presented to concerned students third-year (undergraduate physics students) before they studied the subject and after studying it. We note that these third-year students had had, as an introduction, a deep discussion of the meaning of quantum mechanical concepts for about one hour and a half a week during one month. To compare the results and show the importance of the epistemological and educational aspects, we presented again the same questionnaire to fifth-year physics students (B.Sc degree). We mention that the latter learned Quantum Mechanics without an epistemological introduction of the basic quantum mechanical concepts. Before giving our epistemological and didactical analysis of the results, we give a brief review of a previous didactical study related to the subject made by other authors. We conclude by giving some suggestions which we think are necessary in teaching Quantum Mechanics.