Verfügbarkeit: Concepts in quantum mechanics

Concepts in quantum mechanics:

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Bibliographische Detailangaben
Hauptverfasser:	Mathur, Vishnu Swarup (VerfasserIn), Singh, Surendra (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton, Fla. [u.a.] CRC Press, Chapman & Hall 2009
Schriftenreihe:	CRC series in pure and applied physics
Schlagworte:	Quantum theory Quantentheorie Quantenmechanik Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XV, 598 S. graph. Darst.
ISBN:	9781420078725

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Datensatz im Suchindex

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adam_text	Contents Preface ......................................... xiii Acknowledgments ................................... xv 1 NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS 1 1.1 Inadequacy of Classical Description for Small Systems ........... 1 1.1.1 Planck s Formula for Energy Distribution in Black-body Radiation 1 1.1.2 de Broglie Relation and Wave Nature of Material Particles ..... 2 1.1.3 The Photo-electric Effect ....................... 3 1.1.4 The Compton Effect .......................... 4 1.1.5 Ritz Combination Principle ...................... 6 1.2 Basis of Quantum Mechanics ......................... 9 1.2.1 Principle of Superposition of States .................. 9 1.2.2 Heisenberg Uncertainty Relations ................... 12 1.3 Representation of States ............................ 14 1.4 Dual Vectors: Bra and Ket Vectors ...................... 15 1.5 Linear Operators ................................ 15 1.5.1 Properties of a Linear Operator .................... 16 1.6 Adjoint of a Linear Operator ......................... 16 1.7 Eigenvalues and Eigenvectors of a Linear Operator ............. 18 1.8 Physical Interpretation ............................. 20 1.8.1 Physical Interpretation of Eigenstates and Eigenvalues ....... 20 1.8.2 Physical Meaning of the Orthogonality of States .......... 21 1.9 Observables and Completeness Criterion ................... 21 1.10 Commutativity and Compatibility of Observables .............. 23 1.11 Position and Momentum Commutation Relations .............. 24 1.12 Commutation Relation and the Uncertainty Product ............ 26 Appendix 1A1: Basic Concepts in Classical Mechanics .............. 31 1A1.1 Lagrange Equations of Motion .................... 31 1A1.2 Classical Dynamical Variables ..................... 32 2 REPRESENTATION THEORY 35 2.1 Meaning of Representation ........................... 35 2.2 How to Set up a Representation ........................ 35 2.3 Representatives of a Linear Operator ..................... 37 2.4 Change of Representation ........................... 40 2.5 Coordinate Representation ........................... 43 2.5.1 Physical Interpretation of the Wave Function ............ 44 2.6 Replacement of Momentum Observable ρ by —ifijp ............. 45 2.7 Integral Representation of Dirac Bracket (A2¡ F A ) ........... 50 2.8 The Momentum Representation ........................ 52 2.8.1 Physical Interpretation of Φ(ρι .p2 , ·· -p¡) .............. 52 2.9 Dirac Delta Function .............................. 53 2.9.1 Three-dimensional Delta Function .................. 55 2.9.2 Normalization of a Plane Wave .................... 56 2.10 Relation between the Coordinate and Momentum Representations .... 56 EQUATIONS OF MOTION 67 3.1 Schrödinger Equation of Motion ........................ 67 3.2 Schrödinger Equation in the Coordinate Representation .......... 69 3.3 Equation of Continuity ............................. 70 3.4 Stationary States ................................ 71 3.5 Time-independent Schrödinger Equation in the Coordinate Representation 72 3.6 Time-independent Schrödinger Equation in the Momentum Representation 74 3.6.1 Two-body Bound State Problem (in Momentum Representation) for Non-local Separable Potential ..................... 76 3.7 Time-independent Schrödinger Equation in Matrix Form .......... 77 3.8 The Heisenberg Picture ............................ 79 3.9 The Interaction Picture ............................ 81 Appendix 3A1: Matrices ............................... 86 3A1.1 Characteristic Equation of a Matrix ................. 86 3A1.2 Similarity (and Unitary) Transformation of Matrices ........ 87 3A1.3 Diagonalization of a Matrix ...................... 87 PROBLEMS OF ONE-DIMENSIONAL POTENTIAL BARRIERS 89 4.1 Motion of a Particle across a Potential Step ................. 90 4.2 Passage of a Particle through a Potential Barrier of Finite Extent ..... 94 4.3 Tunneling of a Particle through a Potential Barrier ............. 99 4.4 Bound States in a One-dimensional Square Potential Well ......... 103 4.5 Motion of a Particle in a Periodic Potential ................. 107 BOUND STATES OF SIMPLE SYSTEMS 115 5.1 Introduction ................................... 115 5.2 Motion of a Particle in a Box ......................... 115 5.2.1 Density of States ............................ 117 5.3 Simple Harmonic Oscillator .......................... 118 5.4 Operator Formulation of the Simple Harmonic Oscillator Problem .... 122 5.4.1 Physical Meaning of the Operators ã and â^ ............. 123 5.4.2 Occupation Number Representation (ONR) ............. 125 5.5 Bound State of a Two-particle System with Central Interaction ...... 126 5.6 Bound States of Hydrogen (or Hydrogen-like) Atoms ............ 131 5.7 The Deuteron Problem ............................. 137 5.8 Energy Levels in a Three-dimensional Square Well: General Case ..... 144 5.9 Energy Levels in an Isotropie Harmonic Potential Well ........... 147 Appendix 5A1: Special Functions .......................... 156 5A1.1 Legendre and Associated Legendre Equations ............ 156 5A1.2 Spherical Harmonics .......................... 159 5A1.3 Laguerre and Associated Laguerre Equations ............ 162 5A1.4 Hermite Equation ............................ 166 5A1.5 Bessel Equation ............................. 169 Appendix 5A2: Orthogonal Curvilinear Coordinate Systems ........... 174 5A2.1 Spherical Polar Coordinates ...................... 174 5A2.2 Cylindrical Coordinates ........................ 175 5A2.3 Parabolic Coordinates ......................... 177 5A2.4 General Features of Orthogonal Curvilinear System of Coordinates 178 SYMMETRIES AND CONSERVATION LAWS 181 6.1 Symmetries and Their Group Properties ................... 181 6.2 Symmetries in a Quantum Mechanical System ................ 182 6.3 Basic Symmetry Groups of the Hamiltonian and Conservation Laws . . . 183 6.3.1 Space Translation Symmetry ..................... 184 6.3.2 Time Translation Symmetry ...................... 185 6.3.3 Spatial Rotation Symmetry ...................... 185 6.4 Lie Groups and Their Generators ....................... 188 6.5 Examples of Lie Group ............................. 191 6.5.1 Proper Rotation Group Д(3) (or Special Orthogonal Group 50(3)) 191 6.5.2 The SU(2) Group ............................ 193 6.5.3 Isospin and SU(2) Symmetry ..................... 194 Appendix 6A1: Groups and Representations .................... 199 ANGULAR MOMENTUM IN QUANTUM MECHANICS 203 7.1 Introduction ................................... 203 7.2 Raising and Lowering Operators ....................... 206 7.3 Matrix Representation of Angular Momentum Operators .......... 208 7.4 Matrix Representation of Eigenstates of Angular Momentum ....... 209 7.5 Coordinate Representation of Angular Momentum Operators and States . 212 7.6 General Rotation Group and Rotation Matrices ............... 214 7.6.1 Rotation Matrices ........................... 217 7.7 Coupling of Two Angular Momenta ...................... 218 7.8 Properties of Clebsch-Gordan Coefficients .................. 219 7.8.1 The Vector Model of the Atom .................... 221 7.8.2 Projection Theorem for Vector Operators .............. 221 7.9 Coupling of Three Angular Momenta ..................... 227 7.10 Coupling of Four Angular Momenta (L - S and j— j Coupling) ..... 228 APPROXIMATION METHODS 235 8.1 Introduction ................................... 235 8.2 Non-degenerate Time-independent Perturbation Theory .......... 236 8.3 Time-independent Degenerate Perturbation Theory ............. 242 8.4 The Zeeman Effect ............................... 249 8.5 WKBJ Approximation ............................. 254 8.6 Particle in a Potential Well .......................... 262 8.7 Application of WKBJ Approximation to α -decay .............. 264 8.8 The Variational Method ............................ 267 8.9 The Problem of the Hydrogen Molecule ................... 270 8.10 System of n Identical Particles: Symmetric and Anti-symmetric States . . 274 8.11 Excited States of the Helium Atom ...................... 278 8.12 Statistical (Thomas-Fermi) Model of the Atom ............... 280 8.13 Hartree s Self-consistent Field Method for Multi-electron Atoms ...... 281 8.14 Hartree-Fock Equations ............................ 285 8.15 Occupation Number Representation ..................... 290 QUANTUM THEORY OF SCATTERING 299 9.1 Introduction ................................... 299 9.2 Laboratory and Center-of-mass (CM) Reference Frames .......... 300 9.2.1 Cross-sections in the CM and Laboratory Frames .......... 302 9.3 Scattering Equation and the Scattering Amplitude ............. 303 9.4 Partial Waves and Phase Shifts ........................ 306 9.5 Calculation of Phase Shift ........................... 311 9.6 Phase Shifts for Some Simple Potential Forms ................ 313 9.7 Scattering due to Coulomb Potential ..................... 320 9.8 The Integral Form of Scattering Equation .................. 324 9.8.1 Scattering Amplitude ......................... 327 9.9 Lippmann-Schwinger Equation and the Transition Operator ........ 329 9.10 Born Expansion ................................. 332 9.10.1 Born Approximation .......................... 332 9.10.2 Validity of Born Approximation .................... 334 9.10.3 Born Approximation and the Method of Partial Waves ....... 337 Appendix 9A1: The Calculus of Residues ...................... 342 10 TIME-DEPENDENT PERTURBATION METHODS 351 10.1 Introduction ................................... 351 10.2 Perturbation Constant over an Interval of Time ............... 353 10.3 Harmonic Perturbation: Semi-classical Theory of Radiation ........ 358 10.4 Einstein Coefficients .............................. 363 10.5 Multipole Transitions .............................. 365 10.6 Electric Dipole Transitions in Atoms and Selection Rules .......... 366 10.7 Photo-electric Effect .............................. 368 10.8 Sudden and Adiabatic Approximations .................... 369 10.9 Second Order Effects .............................. 373 11 THE THREE-BODY PROBLEM 377 11.1 Introduction ................................... 377 11.2 Eyges Approach ................................. 377 11.3 Mitra s Approach ................................ 381 11.4 Faddeev s Approach .............................. 385 11.5 Faddeev Equations in Momentum Representation .............. 391 11.6 Faddeev Equations for a Three-body Bound System ............ 393 11.7 Alt, Grassberger and Sandhas (AGS) Equations ............... 396 12 RELATIVISTIC QUANTUM MECHANICS 403 12.1 Introduction ................................... 403 12.2 Dirac Equation ................................. 405 12.3 Spin of the Electron .............................. 408 12.4 Free Particle (Plane Wave) Solutions of Dirac Equation .......... 409 12.5 Dirac Equation for a Zero Mass Particle ................... 413 12.6 Zitterbewegung and Negative Energy Solutions ............... 415 12.7 Dirac Equation for an Electron in an Electromagnetic Field ........ 417 12.8 Invariance of Dirac Equation ......................... 422 12.9 Dirac Bilinear Covariants ........................... 427 12.10 Dirac Electron in a Spherically Symmetric Potential ............ 428 12.11 Charge Conjugation. Parity and Time Reversal Invariance ......... 436 Appendix 12A1: Theory of Special Relativity .................... 445 12A1.1 Lorentz Transformation ........................ 445 12 Al. 2 Minkowski Space-Time Continuum .................. 448 12A1.3 Four-vectors in Relativistic Mechanics ................ 450 12A1.4 Covariant Form of Maxwell s Equations ............... 452 13 QUANTIZATION OF RADIATION FIELD 455 13.1 Introduction ................................... 455 13.2 Radiation Field as a Swarm of Oscillators .................. 455 13.3 Quantization of Radiation Field ........................ 459 13.4 Interaction of Matter with Quantized Radiation Field ........... 462 13.5 Applications ................................... 466 13.6 Atomic Level Shift: Lamb-Retherford Shift ................. 476 13.7 Compton Scattering .............................. 482 Appendix 13A1: Electromagnetic Field in Coulomb Gauge ............ 497 14 SECOND QUANTIZATION 501 14.1 Introduction ................................... 501 14.2 Classical Concept of Field ........................... 502 14.3 Analogy of Field and Particle Mechanics ................... 504 14.4 Field Equations from Lagrangian Density .................. 507 14.4.1 Electromagnetic Field ......................... 507 14.4.2 Klein-Gordon Field (Real and Complex) ............... 508 14.4.3 Dirac Field ............................... 510 14.5 Quantization of a Real Scalar (KG) Field .................. 511 14.6 Quantization of Complex Scalar (KG) Field ................. 514 14.7 Dirac Field and Its Quantization ....................... 519 14.8 Positron Operators and Spinors ........................ 522 14.8.1 Equations Satisfied by Electron and Positron Spinors ........ 524 14.8.2 Projection Operators .......................... 525 14.8.3 Electron Vacuum ............................ 527 14.9 Interacting Fields and the Covariant Perturbation Theory ......... 527 14.9.1 U Matrix ................................ 529 14.9.2 S Matrix and Iterative Expansion of S Operator .......... 531 14.9.3 Time-ordered Operator Product in Terms of Normal Constituents 532 14.10 Second Order Processes in Electrodynamics ................. 534 14.10.1 Feynman Diagrams ........................... 536 14.11 Amplitude for Compton Scattering ...................... 540 14.12 Feynman Graphs ................................ 545 14.12.1 Compton Scattering Amplitude Using Feynman Rules ....... 546 14.12.2 Electron-positron (e~e+) Pair Annihilation ............. 547 14.12.3 Two-photon Annihilation Leading to (e~e+) Pair Creation .... 549 14.12.4 Möller (e є ) Scattering ....................... 550 14.12.5 Bhabha (e~e+) Scattering ....................... 550 14.13 Calculation of the Cross-section of Compton Scattering .......... 551 14.14 Cross-sections for Other Electromagnetic Processes ............. 557 14.14.1 Electron-Positron Pair Annihilation (Electron at Rest) ....... 557 14.14.2 Möller (Ce-) and Bhabha (e~c+) Scattering ............ 558 Appendix 14 Al: Calculus of Variation and Euler- Lagrange Equations ...... 564 Appendix 14A2: Functional and Functional Derivatives ............. 567 Appendix 14A3: Interaction of the Electron and Radiation Fields ........ 569 Appendix 14A4: On the Convergence of Iterative Expansion of the 5 Operator . 570 15 EPILOGUE 573 15.1 Introduction ................................... 573 15.2 EPR Gedanken Experiment .......................... 574 15.3 Einstein-Podolsky-Rosen-Bohm Gedanken Experiment ........... 577 15.4 Theory of Hidden Variables and Bell s Inequality .............. 579 15.5 Clauser-Horne Form of Bell s Inequality and Its Violation in Two-photon Correlation Experiments ............................ 584 General References .................................. 591 Index 593
adam_txt	Contents Preface . xiii Acknowledgments . xv 1 NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS 1 1.1 Inadequacy of Classical Description for Small Systems . 1 1.1.1 Planck's Formula for Energy Distribution in Black-body Radiation 1 1.1.2 de Broglie Relation and Wave Nature of Material Particles . 2 1.1.3 The Photo-electric Effect . 3 1.1.4 The Compton Effect . 4 1.1.5 Ritz Combination Principle . 6 1.2 Basis of Quantum Mechanics . 9 1.2.1 Principle of Superposition of States . 9 1.2.2 Heisenberg Uncertainty Relations . 12 1.3 Representation of States . 14 1.4 Dual Vectors: Bra and Ket Vectors . 15 1.5 Linear Operators . 15 1.5.1 Properties of a Linear Operator . 16 1.6 Adjoint of a Linear Operator . 16 1.7 Eigenvalues and Eigenvectors of a Linear Operator . 18 1.8 Physical Interpretation . 20 1.8.1 Physical Interpretation of Eigenstates and Eigenvalues . 20 1.8.2 Physical Meaning of the Orthogonality of States . 21 1.9 Observables and Completeness Criterion . 21 1.10 Commutativity and Compatibility of Observables . 23 1.11 Position and Momentum Commutation Relations . 24 1.12 Commutation Relation and the Uncertainty Product . 26 Appendix 1A1: Basic Concepts in Classical Mechanics . 31 1A1.1 Lagrange Equations of Motion . 31 1A1.2 Classical Dynamical Variables . 32 2 REPRESENTATION THEORY 35 2.1 Meaning of Representation . 35 2.2 How to Set up a Representation . 35 2.3 Representatives of a Linear Operator . 37 2.4 Change of Representation . 40 2.5 Coordinate Representation . 43 2.5.1 Physical Interpretation of the Wave Function . 44 2.6 Replacement of Momentum Observable ρ by —ifijp . 45 2.7 Integral Representation of Dirac Bracket (A2¡ F \A\) . 50 2.8 The Momentum Representation . 52 2.8.1 Physical Interpretation of Φ(ρι .p2 , ·· -p¡) . 52 2.9 Dirac Delta Function . 53 2.9.1 Three-dimensional Delta Function . 55 2.9.2 Normalization of a Plane Wave . 56 2.10 Relation between the Coordinate and Momentum Representations . 56 EQUATIONS OF MOTION 67 3.1 Schrödinger Equation of Motion . 67 3.2 Schrödinger Equation in the Coordinate Representation . 69 3.3 Equation of Continuity . 70 3.4 Stationary States . 71 3.5 Time-independent Schrödinger Equation in the Coordinate Representation 72 3.6 Time-independent Schrödinger Equation in the Momentum Representation 74 3.6.1 Two-body Bound State Problem (in Momentum Representation) for Non-local Separable Potential . 76 3.7 Time-independent Schrödinger Equation in Matrix Form . 77 3.8 The Heisenberg Picture . 79 3.9 The Interaction Picture . 81 Appendix 3A1: Matrices . 86 3A1.1 Characteristic Equation of a Matrix . 86 3A1.2 Similarity (and Unitary) Transformation of Matrices . 87 3A1.3 Diagonalization of a Matrix . 87 PROBLEMS OF ONE-DIMENSIONAL POTENTIAL BARRIERS 89 4.1 Motion of a Particle across a Potential Step . 90 4.2 Passage of a Particle through a Potential Barrier of Finite Extent . 94 4.3 Tunneling of a Particle through a Potential Barrier . 99 4.4 Bound States in a One-dimensional Square Potential Well . 103 4.5 Motion of a Particle in a Periodic Potential . 107 BOUND STATES OF SIMPLE SYSTEMS 115 5.1 Introduction . 115 5.2 Motion of a Particle in a Box . 115 5.2.1 Density of States . 117 5.3 Simple Harmonic Oscillator . 118 5.4 Operator Formulation of the Simple Harmonic Oscillator Problem . 122 5.4.1 Physical Meaning of the Operators ã and â^ . 123 5.4.2 Occupation Number Representation (ONR) . 125 5.5 Bound State of a Two-particle System with Central Interaction . 126 5.6 Bound States of Hydrogen (or Hydrogen-like) Atoms . 131 5.7 The Deuteron Problem . 137 5.8 Energy Levels in a Three-dimensional Square Well: General Case . 144 5.9 Energy Levels in an Isotropie Harmonic Potential Well . 147 Appendix 5A1: Special Functions . 156 5A1.1 Legendre and Associated Legendre Equations . 156 5A1.2 Spherical Harmonics . 159 5A1.3 Laguerre and Associated Laguerre Equations . 162 5A1.4 Hermite Equation . 166 5A1.5 Bessel Equation . 169 Appendix 5A2: Orthogonal Curvilinear Coordinate Systems . 174 5A2.1 Spherical Polar Coordinates . 174 5A2.2 Cylindrical Coordinates . 175 5A2.3 Parabolic Coordinates . 177 5A2.4 General Features of Orthogonal Curvilinear System of Coordinates 178 SYMMETRIES AND CONSERVATION LAWS 181 6.1 Symmetries and Their Group Properties . 181 6.2 Symmetries in a Quantum Mechanical System . 182 6.3 Basic Symmetry Groups of the Hamiltonian and Conservation Laws . . . 183 6.3.1 Space Translation Symmetry . 184 6.3.2 Time Translation Symmetry . 185 6.3.3 Spatial Rotation Symmetry . 185 6.4 Lie Groups and Their Generators . 188 6.5 Examples of Lie Group . 191 6.5.1 Proper Rotation Group Д(3) (or Special Orthogonal Group 50(3)) 191 6.5.2 The SU(2) Group . 193 6.5.3 Isospin and SU(2) Symmetry . 194 Appendix 6A1: Groups and Representations . 199 ANGULAR MOMENTUM IN QUANTUM MECHANICS 203 7.1 Introduction . 203 7.2 Raising and Lowering Operators . 206 7.3 Matrix Representation of Angular Momentum Operators . 208 7.4 Matrix Representation of Eigenstates of Angular Momentum . 209 7.5 Coordinate Representation of Angular Momentum Operators and States . 212 7.6 General Rotation Group and Rotation Matrices . 214 7.6.1 Rotation Matrices . 217 7.7 Coupling of Two Angular Momenta . 218 7.8 Properties of Clebsch-Gordan Coefficients . 219 7.8.1 The Vector Model of the Atom . 221 7.8.2 Projection Theorem for Vector Operators . 221 7.9 Coupling of Three Angular Momenta . 227 7.10 Coupling of Four Angular Momenta (L - S and j— j Coupling) . 228 APPROXIMATION METHODS 235 8.1 Introduction . 235 8.2 Non-degenerate Time-independent Perturbation Theory . 236 8.3 Time-independent Degenerate Perturbation Theory . 242 8.4 The Zeeman Effect . 249 8.5 WKBJ Approximation . 254 8.6 Particle in a Potential Well . 262 8.7 Application of WKBJ Approximation to α -decay . 264 8.8 The Variational Method . 267 8.9 The Problem of the Hydrogen Molecule . 270 8.10 System of n Identical Particles: Symmetric and Anti-symmetric States . . 274 8.11 Excited States of the Helium Atom . 278 8.12 Statistical (Thomas-Fermi) Model of the Atom . 280 8.13 Hartree's Self-consistent Field Method for Multi-electron Atoms . 281 8.14 Hartree-Fock Equations . 285 8.15 Occupation Number Representation . 290 QUANTUM THEORY OF SCATTERING 299 9.1 Introduction . 299 9.2 Laboratory and Center-of-mass (CM) Reference Frames . 300 9.2.1 Cross-sections in the CM and Laboratory Frames . 302 9.3 Scattering Equation and the Scattering Amplitude . 303 9.4 Partial Waves and Phase Shifts . 306 9.5 Calculation of Phase Shift . 311 9.6 Phase Shifts for Some Simple Potential Forms . 313 9.7 Scattering due to Coulomb Potential . 320 9.8 The Integral Form of Scattering Equation . 324 9.8.1 Scattering Amplitude . 327 9.9 Lippmann-Schwinger Equation and the Transition Operator . 329 9.10 Born Expansion . 332 9.10.1 Born Approximation . 332 9.10.2 Validity of Born Approximation . 334 9.10.3 Born Approximation and the Method of Partial Waves . 337 Appendix 9A1: The Calculus of Residues . 342 10 TIME-DEPENDENT PERTURBATION METHODS 351 10.1 Introduction . 351 10.2 Perturbation Constant over an Interval of Time . 353 10.3 Harmonic Perturbation: Semi-classical Theory of Radiation . 358 10.4 Einstein Coefficients . 363 10.5 Multipole Transitions . 365 10.6 Electric Dipole Transitions in Atoms and Selection Rules . 366 10.7 Photo-electric Effect . 368 10.8 Sudden and Adiabatic Approximations . 369 10.9 Second Order Effects . 373 11 THE THREE-BODY PROBLEM 377 11.1 Introduction . 377 11.2 Eyges Approach . 377 11.3 Mitra's Approach . 381 11.4 Faddeev's Approach . 385 11.5 Faddeev Equations in Momentum Representation . 391 11.6 Faddeev Equations for a Three-body Bound System . 393 11.7 Alt, Grassberger and Sandhas (AGS) Equations . 396 12 RELATIVISTIC QUANTUM MECHANICS 403 12.1 Introduction . 403 12.2 Dirac Equation . 405 12.3 Spin of the Electron . 408 12.4 Free Particle (Plane Wave) Solutions of Dirac Equation . 409 12.5 Dirac Equation for a Zero Mass Particle . 413 12.6 Zitterbewegung and Negative Energy Solutions . 415 12.7 Dirac Equation for an Electron in an Electromagnetic Field . 417 12.8 Invariance of Dirac Equation . 422 12.9 Dirac Bilinear Covariants . 427 12.10 Dirac Electron in a Spherically Symmetric Potential . 428 12.11 Charge Conjugation. Parity and Time Reversal Invariance . 436 Appendix 12A1: Theory of Special Relativity . 445 12A1.1 Lorentz Transformation . 445 12 Al. 2 Minkowski Space-Time Continuum . 448 12A1.3 Four-vectors in Relativistic Mechanics . 450 12A1.4 Covariant Form of Maxwell's Equations . 452 13 QUANTIZATION OF RADIATION FIELD 455 13.1 Introduction . 455 13.2 Radiation Field as a Swarm of Oscillators . 455 13.3 Quantization of Radiation Field . 459 13.4 Interaction of Matter with Quantized Radiation Field . 462 13.5 Applications . 466 13.6 Atomic Level Shift: Lamb-Retherford Shift . 476 13.7 Compton Scattering . 482 Appendix 13A1: Electromagnetic Field in Coulomb Gauge . 497 14 SECOND QUANTIZATION 501 14.1 Introduction . 501 14.2 Classical Concept of Field . 502 14.3 Analogy of Field and Particle Mechanics . 504 14.4 Field Equations from Lagrangian Density . 507 14.4.1 Electromagnetic Field . 507 14.4.2 Klein-Gordon Field (Real and Complex) . 508 14.4.3 Dirac Field . 510 14.5 Quantization of a Real Scalar (KG) Field . 511 14.6 Quantization of Complex Scalar (KG) Field . 514 14.7 Dirac Field and Its Quantization . 519 14.8 Positron Operators and Spinors . 522 14.8.1 Equations Satisfied by Electron and Positron Spinors . 524 14.8.2 Projection Operators . 525 14.8.3 Electron Vacuum . 527 14.9 Interacting Fields and the Covariant Perturbation Theory . 527 14.9.1 U Matrix . 529 14.9.2 S Matrix and Iterative Expansion of S Operator . 531 14.9.3 Time-ordered Operator Product in Terms of Normal Constituents 532 14.10 Second Order Processes in Electrodynamics . 534 14.10.1 Feynman Diagrams . 536 14.11 Amplitude for Compton Scattering . 540 14.12 Feynman Graphs . 545 14.12.1 Compton Scattering Amplitude Using Feynman Rules . 546 14.12.2 Electron-positron (e~e+) Pair Annihilation . 547 14.12.3 Two-photon Annihilation Leading to (e~e+) Pair Creation . 549 14.12.4 Möller (e" є") Scattering . 550 14.12.5 Bhabha (e~e+) Scattering . 550 14.13 Calculation of the Cross-section of Compton Scattering . 551 14.14 Cross-sections for Other Electromagnetic Processes . 557 14.14.1 Electron-Positron Pair Annihilation (Electron at Rest) . 557 14.14.2 Möller (Ce-) and Bhabha (e~c+) Scattering . 558 Appendix 14 Al: Calculus of Variation and Euler- Lagrange Equations . 564 Appendix 14A2: Functional and Functional Derivatives . 567 Appendix 14A3: Interaction of the Electron and Radiation Fields . 569 Appendix 14A4: On the Convergence of Iterative Expansion of the 5 Operator . 570 15 EPILOGUE 573 15.1 Introduction . 573 15.2 EPR Gedanken Experiment . 574 15.3 Einstein-Podolsky-Rosen-Bohm Gedanken Experiment . 577 15.4 Theory of Hidden Variables and Bell's Inequality . 579 15.5 Clauser-Horne Form of Bell's Inequality and Its Violation in Two-photon Correlation Experiments . 584 General References . 591 Index 593
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index_date	2024-07-02T22:11:35Z
indexdate	2024-07-09T21:22:03Z
institution	BVB
isbn	9781420078725
language	English
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physical	XV, 598 S. graph. Darst.
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publisher	CRC Press, Chapman & Hall
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series2	CRC series in pure and applied physics
spelling	Mathur, Vishnu Swarup Verfasser aut Concepts in quantum mechanics Vishnu Swarup Mathur ; Surendra Singh Boca Raton, Fla. [u.a.] CRC Press, Chapman & Hall 2009 XV, 598 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRC series in pure and applied physics Quantum theory Quantentheorie Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenmechanik (DE-588)4047989-4 s DE-604 Singh, Surendra Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016761944&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Mathur, Vishnu Swarup Singh, Surendra Concepts in quantum mechanics Quantum theory Quantentheorie Quantenmechanik (DE-588)4047989-4 gnd
subject_GND	(DE-588)4047989-4 (DE-588)4123623-3
title	Concepts in quantum mechanics
title_auth	Concepts in quantum mechanics
title_exact_search	Concepts in quantum mechanics
title_exact_search_txtP	Concepts in quantum mechanics
title_full	Concepts in quantum mechanics Vishnu Swarup Mathur ; Surendra Singh
title_fullStr	Concepts in quantum mechanics Vishnu Swarup Mathur ; Surendra Singh
title_full_unstemmed	Concepts in quantum mechanics Vishnu Swarup Mathur ; Surendra Singh
title_short	Concepts in quantum mechanics
title_sort	concepts in quantum mechanics
topic	Quantum theory Quantentheorie Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Quantum theory Quantentheorie Quantenmechanik Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016761944&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT mathurvishnuswarup conceptsinquantummechanics AT singhsurendra conceptsinquantummechanics

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