04192nam 2200637Ia 450 991045743030332120200520144314.01-84816-798-9(CKB)2550000000086855(EBL)846118(OCoLC)858227751(SSID)ssj0000600047(PQKBManifestationID)12257071(PQKBTitleCode)TC0000600047(PQKBWorkID)10598727(PQKB)10131364(MiAaPQ)EBC846118(WSP)0000P811(Au-PeEL)EBL846118(CaPaEBR)ebr10525604(CaONFJC)MIL498440(EXLCZ)99255000000008685520120209d2012 uy 0engur|n|---|||||txtccrThe supersymmetric Dirac equation[electronic resource] the application to hydrogenic atoms /Allen HirshfeldLondon Imperial College Press ;Singapore ;Hackensack, NJ Distributed by World Scientificc20121 online resource (216 p.)Description based upon print version of record.1-84816-797-0 Includes bibliographical references and index.Preface; Contents; List of Figures; 1. Introduction; 2. The Classical Kepler Problem; 2.1 Central Forces; 2.2 The Laplace Vector; 3. Symmetry of the Classical Problem; 3.1 Lie Groups and Lie Algebras; 3.2 Some Special Lie Algebras; 3.3 Poisson Brackets; 3.4 The Inverse Square Law; 4. From Solar Systems to Atoms; 4.1 Rutherford Scattering; 4.2 Conservation of the Laplace Vector; 4.3 The Differential Cross Section; 5. The Bohr Model; 5.1 Spectroscopic Series; 5.2 The Postulates of the Model; 5.3 The Predictions of the Model; 5.4 Correction for Finite Nuclear Mass6. Interpretation of the Quantum Rules6.1 The Sommerfeld-Wilson Quantization Conditions; 6.2 de Broglie's Wave Interpretation; 7. Sommerfeld's Model for Non-Relativistic Electrons; 7.1 Assumptions of the Model; 7.2 Results of the Model for Non-Relativistic Hydrogen Atoms; 7.3 The Eccentricity; 8. Quantum Mechanics of Hydrogenic Atoms; 8.1 Quantization; 8.2 Quantum Mechanical Relation Between |A| and L; 8.3 Pauli's Hydrogenic Realization of so(4); 8.4 so(4) and the Spectrum of Hydrogenic Atoms; 9. The Schrödinger Equation and the Confluent Hypergeometric Functions12. Sommerfeld's Derivation of the Relativistic Energy Level Formula12.1 Assumptions of the Model; 12.2 The Energies of the Bound States; 13. The Dirac Equation; 13.1 The Hamiltonian; 13.2 Total Angular Momentum; 13.3 The Dirac Operator; 13.4 A Complete Set of Mutually Commuting Operators; 13.5 The Dirac Spinors; 13.6 The Radial Equations in Polar Coordinates; 14. The Primary Supersymmetry of the Dirac Equation; 14.1 A Derivation of the Johnson-Lippmann Operator; 14.2 Commutation and Anticommutation Relations of the Johnson-Lippmann Operator; 14.3 Eccentricity17.2 Eigenfunctions of the Operators G andThe solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book. Dirac equationSupersymmetryQuantum field theoryElectronic books.Dirac equation.Supersymmetry.Quantum field theory.530.1209530.124Hirshfeld Allen C477215MiAaPQMiAaPQMiAaPQBOOK9910457430303321The supersymmetric Dirac equation1919481UNINA