Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics : non-relativistic and relativistic / Tamar T. Khachidze and Anzor A. Khelashvili.

Format:

Book

Author/Creator:

Khachidze, Tamar T.

Contributor:

Khelashvili, A. A.

Language:

English

Subjects (All):

Symmetry (Physics).

Mechanics.

Quantum theory.

Physical Description:

1 online resource (168 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2008.

Language Note:

English

Summary:

The purpose of this book is to develop a systematic theory for the hidden symmetry generators, which are simultaneously the odd generators of superalgebra in relativistic quantum mechanics. It is devoted to the description of so-called hidden symmetry of the Kepler problem in classical and quantum mechanics.

Contents:

Intro

DYNAMICAL SYMMETRY OF THEKEPLER-COULOMB PROBLEM INCLASSICAL AND QUANTUMMECHANICS: NON-RELATIVISTICAND RELATIVISTIC

CONTENTS

ABOUT THE AUTHORS

PREFACE

INTRODUCTION

THE GENERAL CONCEPTS OF DYNAMICAL SYMMETRIES

REFERENCES

HIDDEN (DYNAMICAL) SYMMETRIES IN CLASSICALMECHANICS

I.1. CONSTANTS OF MOTION AS GENERATORS OF INFINITESIMALTRANSFORMATIONS

Remark

I.2. DERIVATION OF LRL VECTOR

I.3. APPLICATIONS OF LRL VECTOR IN CLASSICAL PHYSICS

(I) LRL Vector and the Orbit Equation

(II). Algebraic Aspects of the Kepler Problem

I.4. DYNAMICAL SYMMETRY FOR THE ISOTROPICHARMONIC OSCILLATOR

I.5. POSSIBLE GENERALIZATIONS OF DYNAMICAL SYMMETRIES

Comments

I.6. APPLICATION OF THE DYNAMICAL EVOLUTION OF LRLVECTOR IN GENERAL CENTRAL CASE [12]

Equations of Motion for General Central Forces

Equations of Motion for Arbitrary Forces

Summary Comments on Dynamical Symmetries in Classical(Non-Relativistic) Mechanics

HIDDEN SYMMETRY IN CLASSICAL RELATIVISTICMECHANICS

II.1. AUXILIARY PROBLEM: LRL VECTOR FOR A MODIFIEDKEPLER PROBLEM

II.2. THE LAPLACE-RUNGE-LENZ VECTOR AND THE LORENTZBOOST

II.3. POST-NEWTONIAN EXTENSIONS OF THE LRL VECTOR

II.4. RELATIVISTIC KEPLER PROBLEM

DYNAMICAL SYMMETRIES IN NON-RELATIVISTICQUANTUM MECHANICS

III.1. THE HYDROGEN ATOM (GENERAL CONSIDERATION)

Algebraic Aspects of the Hydrogen Problem [2]

III.2. THE HYDROGEN ATOM IN THE MOMENTUM

Representation

Example of Application of The Momentum Representation:Dynamical Symmetry of a Three Dimensional Wick-Cutkosky Problem [7]

III. 3. THE HYDROGEN ATOM AND THE LORENTZ GROUP

III. 4. THREE DIMENSIONAL ISOTROPIC HARMONIC OSCILLATORAND SU(3) [14]

A NEW KIND OF DYNAMICAL SYMMETRY -SUPERSYMMETRY

IV.1 SUPERSYMMETRIC QUANTUM MECHANICS.

IV.2. SUPERSYMMETRY AND THE RADIAL PROBLEM

IV. 3. EXACT SUPERSYMMETRY IN THE NON-RELATIVISTICHYDROGEN ATOM

RELATIVISTIC QUANTUM MECHANICS

V.1. SUPERSYMMETRY IN THE DIRAC EQUATION FOR THECOULOMB POTENTIAL

APPENDIX: SHAPE INVARIANCE (SI)

V. 2. AN "ACCIDENTAL SYMMETRY" OPERATORFOR THE DIRAC EQUATION IN THE COULOMB POTENTIAL -FROM PAULI TO DIRAC

V. 3. PHYSICAL MEANING AND SOME APPLICATIONSOF JOHNSON - LIPPMANN OPERATOR

APPENDIX: CALCULATION OF RELEVANT COMMUTATORS

GENERALIZATIONS TO THE RELATIVISTIC DIRACHAMILTONIAN

VI.1. SUPERSYMMETRY OF THE DIRAC HAMILTONIANFOR GENERAL CENTRAL POTENTIALS

VI.2. WHERE IS THE HARMONIC OSCILLATOR?

VI.3. RELATIVISTIC QUANTUM MECHANICSOF DIRAC OSCILLATOR

VI.4. THE LORENTZ - SCALAR POTENTIALIN THE DIRAC EQUATION

VI.5. ALGEBRAIC DERIVATION OF THE SPECTRUM OF THEDIRAC HAMILTONIAN FOR AN ARBITRARY COMBINATIONOF THE LORENTZ-SCALAR AND LORENTZ-VECTOR COULOMBPOTENTIAL

SOME RECENT DEVELOPMENTS

VII.1 HIDDEN SUPERSYMMETRY OF THE DIRAC-COULOMBPROBLEM AND THE BIEDENHARN APPOACH

VII.2 SOME PRACTICAL GENERALIZATIONS: THE LRL VECTOR INTHE PRESENCE OF AN ELECTRIC FIELD [9]

CONCLUSIONS

BIBLIOGRAPHY (PART I)

PART II

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [129]-143) and index.

ISBN:

1-61324-498-3

OCLC:

923661947