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Autore: |
Khachidze Tamar T
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Titolo: |
Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics [[electronic resource] ] : non-relativistic and relativistic / / Tamar T. Khachidze and Anzor A. Khelashvili
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Pubblicazione: | New York, : Nova Science Publishers, c2008 |
Edizione: | 1st ed. |
Descrizione fisica: | 1 online resource (168 p.) |
Disciplina: | 539.7/25 |
Soggetto topico: | Symmetry (Physics) |
Mechanics | |
Quantum theory | |
Altri autori: |
KhelashviliA. A
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Note generali: | Description based upon print version of record. |
Nota di bibliografia: | Includes bibliographical references (p. [129]-143) and index. |
Nota di contenuto: | 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 -- REFERENCES -- 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 -- REFERENCES -- 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] -- REFERENCES -- 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 -- REFERENCES -- 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 -- REFERENCES -- 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 -- Comments -- REFERENCES -- 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 -- REFERENCES -- BIBLIOGRAPHY (PART I) -- PART II -- INDEX. | |
Titolo autorizzato: | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics ![]() |
ISBN: | 1-61324-498-3 |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910820605403321 |
Lo trovi qui: | Univ. Federico II |
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