LEADER 04925nam 2200577 a 450 001 9910820605403321 005 20240410171010.0 010 $a1-61324-498-3 035 $a(CKB)2550000000044236 035 $a(EBL)3019797 035 $a(SSID)ssj0000522156 035 $a(PQKBManifestationID)12212555 035 $a(PQKBTitleCode)TC0000522156 035 $a(PQKBWorkID)10527655 035 $a(PQKB)10076745 035 $a(MiAaPQ)EBC3019797 035 $a(Au-PeEL)EBL3019797 035 $a(CaPaEBR)ebr10671362 035 $a(OCoLC)923661947 035 $a(EXLCZ)992550000000044236 100 $a20080205d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics$b[electronic resource] $enon-relativistic and relativistic /$fTamar T. Khachidze and Anzor A. Khelashvili 205 $a1st ed. 210 $aNew York $cNova Science Publishers$dc2008 215 $a1 online resource (168 p.) 300 $aDescription based upon print version of record. 311 $a1-60456-499-7 320 $aIncludes bibliographical references (p. [129]-143) and index. 327 $aIntro -- 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. 327 $aIV.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. 606 $aSymmetry (Physics) 606 $aMechanics 606 $aQuantum theory 615 0$aSymmetry (Physics) 615 0$aMechanics. 615 0$aQuantum theory. 676 $a539.7/25 700 $aKhachidze$b Tamar T$01595537 701 $aKhelashvili$b A. A$01595538 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910820605403321 996 $aDynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics$93916520 997 $aUNINA