LEADER 04192nam 2200637Ia 450 001 9910457430303321 005 20200520144314.0 010 $a1-84816-798-9 035 $a(CKB)2550000000086855 035 $a(EBL)846118 035 $a(OCoLC)858227751 035 $a(SSID)ssj0000600047 035 $a(PQKBManifestationID)12257071 035 $a(PQKBTitleCode)TC0000600047 035 $a(PQKBWorkID)10598727 035 $a(PQKB)10131364 035 $a(MiAaPQ)EBC846118 035 $a(WSP)0000P811 035 $a(Au-PeEL)EBL846118 035 $a(CaPaEBR)ebr10525604 035 $a(CaONFJC)MIL498440 035 $a(EXLCZ)992550000000086855 100 $a20120209d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe supersymmetric Dirac equation$b[electronic resource] $ethe application to hydrogenic atoms /$fAllen Hirshfeld 210 $aLondon $cImperial College Press ;$aSingapore ;$aHackensack, NJ $cDistributed by World Scientific$dc2012 215 $a1 online resource (216 p.) 300 $aDescription based upon print version of record. 311 $a1-84816-797-0 320 $aIncludes bibliographical references and index. 327 $aPreface; 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 Mass 327 $a6. 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 Schro?dinger Equation and the Confluent Hypergeometric Functions 327 $a12. 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 Eccentricity 327 $a17.2 Eigenfunctions of the Operators G and 330 $aThe 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. 606 $aDirac equation 606 $aSupersymmetry 606 $aQuantum field theory 608 $aElectronic books. 615 0$aDirac equation. 615 0$aSupersymmetry. 615 0$aQuantum field theory. 676 $a530.1209 676 $a530.124 700 $aHirshfeld$b Allen C$0477215 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457430303321 996 $aThe supersymmetric Dirac equation$91919481 997 $aUNINA