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

• Record Nr.: UNINA9910820605403321
• Autore: Khachidze Tamar T
• Pubbl/distr/stampa: New York, : Nova Science Publishers, c2008
• ISBN: 1-61324-498-3
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (168 p.)
• Altri autori (Persone): KhelashviliA. A
• Disciplina: 539.7/25
• Soggetti: Symmetry (Physics); Mechanics; Quantum theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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.