Intermediate Quantum Mechanics, 3rd Edition (Advanced Books Classics)

Graduate students in both theoretical and experimental physics will find this third edition of Intermediate Quantum Mechanics, refined and updated in 1986, indispensable. The first part of the book deals with the theory of atomic structure, while the second and third parts deal with the relativistic wave equations and introduction to field theory, making Intermediate Quantum Mechanics more complete than any other single-volume work on the subject. CONTENTS 14 Editors' Foreword 8 Preface to First Edition 10 Preface to Second Edition 12 Preface to Third Edition 13 PART I: THEORY OF ATOMIC STRUCTURE 20 Chapter 1: MISCELLANEOUS RESULTS FROM ELEMENTARY QUANTUM MECHANICS 22 Schrödinger Equation 22 Approximate Methods of Solution 24 Constants of Motion 31 Spin 32 Description of Spin 1⁄2 Particles 34 Problems 36 Chapter 2: IDENTICAL PARTICLES AND SYMMETRY 39 Arguments for Simple Symmetry 40 Symmetry for Composite Systems 44 Construction of Symmetrized Wave Functions 44 Statistical Mechanics 45 Experimental Determination of Symmetry 46 Classical Limit 47 Problems 48 Chapter 3: TWO-ELECTRON ATOMS 50 Classification of Solutions 50 Perturbation Calculation 51 Variation Calculation 63 Ionization Potential for Higher Z Atoms 68 Excited States 69 Problems 70 Chapter 4: SELF-CONSISTENT FIELD 72 Intuitive Preliminaries 72 Variation Derivation 74 Matrix Elements Between Determinantal Wave Functions 75 Derivation of the Hartree-Fock Equations 77 Discussion of the Exchange Term 80 Physical Significance of the Eigenvalue 83 Spherical Symmetry and the Hartree-Fock Equations 84 Approximate Treatment of Exchange Term 91 Results of Calculations 94 High n 97 Periodic System 98 Problems 101 Chapter 5: STATISTICAL MODELS 103 Thomas-Fermi Model 103 Solutions of the Thomas-Fermi Equation 106 Determination of Additional Boundary Conditions 107 Applications 109 Validity of the Thomas-Fermi Method 110 Correction for Exchange; The Thomas-Fermi-Dirac Equation 111 Problems 117 Chapter 6: ADDITION OF ANGULAR MOMENTA 120 Angular Momentum 121 Addition of Angular Momenta 123 Clebsch-Gordan Coefficients 125 Special Cases 128 Addition of Angular Momenta for Identical Particles 130 Addition of Angular Momenta for Equivalent Electrons 132 Problems 136 Chapter 7: THEORY OF MULTIPLETS, ELECTROSTATIC INTERACTION 137 Discussion of Matrix Elements 139 Slater Sum Rule 147 Equivalence of Holes and Electrons 150 Evaluation of Integrals 151 Sample Calculation 153 Comparison with Experimental Results 156 Average Energy 158 Configuration Interaction 164 Electron Correlation 165 Problems 168 Chapter 8: THEORY OF MULTIPLETS, SPIN-ORBIT INTERACTION, AND INTERACTIONS WITH EXTERNAL FIELDS 169 Interaction with a Constant External Magnetic Field 169 Spin-Orbit Interaction for Atoms 171 A Theorem About Matrix Elements 176 Evaluation of the Spin-Orbit Interaction 181 Comparison with Experiment 187 Zeeman Effect 188 Paschen-Back Effect: 189 Quadratic Zeeman Effect 190 Stark Effect 192 Problems 194 Chapter 9: MOLECULES 198 Born-Oppenheimer Approximation 198 Hydrogen Molecule 201 Diatomic Molecules 204 Symmetry for Homonuclear Diatomic Molecules 206 Problems 208 PART II: SEMICLASSICAL RADIATION THEORY 210 Chapter 10: SEMICLASSICAL THEORY OF RADIATION 212 Schrödinger Equation 212 Absorption and Induced Emission 214 Monochromatic External Fields 214 Nonmonochromatic External Fields 218 Multipole Transitions 222 Spontaneous Emission 223 Einstein Transition Probabilities 225 Line Breadth 227 Problems 228 Chapter 11: INTENSITY OF RADIATION, SELECTION RULES 230 Sum Rules 230 Summary 236 Many Electrons 237 Hydrogen 238 Selection Rules and Matrix Elements 240 Selection Rules for Many Electrons 244 Higher Moments 246 Absolute Transition Probabilities 248 Problems 251 Chapter 12: PHOTOELECTRIC EFFECT 252 Born Approximation 252 Dipole Approximation 254 Rough Estimate 257 Problems 258 PART III: ATOMIC COLLISIONS 260 Chapter 13: ELASTIC SCATTERING AT HIGH ENERGIES 262 Elastic Scattering in the Born Approximation 263 Calculation of Form Factors 267 Comparison with Experiment 269 Problems 272 Chapter 14: ELASTIC SCATTERING AT LOW ENERGIES 273 Ramsauer-Townsend Effect 278 Polarization of Atom by Incident Particle 282 Problems 284 Chapter 15: FURTHER CORRECTIONS TO ELASTIC SCATTERING FORMULAS 285 Electron Exchange 285 Shadow Scattering 288 Problems 299 Chapter 16: ELASTIC SCATTERING OF SPIN 1⁄2 PARTICLES 300 Generalization 304 Density Matrix 306 Problems 299 Chapter 17: INELASTIC SCATTERING AT HIGH ENERGIES 314 Results of Calculation and Comparison with Experiment 321 Energy Loss of the Incident Particle 322 Problems 328 Chapter 18: INELASTIC SCATTERING AT LOW ENERGIES 329 Validity of Distorted Wave Approximation 333 Results of Calculation and Comparison with Experiment 336 Further Corrections 338 Close Coupling Approximation 338 Collision Complex 339 Problems 340 Chapter 19: SEMICLASSICAL TREATMENT OF INELASTIC SCATTERING 341 Equivalence with Born Approximation 346 Problems 349 Chapter 20: CLASSICAL LIMIT OF QUANTUM MECHANICAL SCATTERING; SUMMARY 350 Forward Scattering 355 Summary of Methods 357 Problems 357 PART IV: RELATIVISTIC EQUATIONS 358 Chapter 21: KLEIN-GORDON EQUATION 360 Physical Interpretation of the Klein-Gordon Equation 361 Interaction with External Electromagnetic Field 363 Coulomb Field 364 Problems 367 Chapter 22: DIRAC EQUATION, FORMAL THEORY 368 Derivation of the Dirac Equation 368 Dirac Matrices I 371 Covariant Form of the Dirac Equation 372 Dirac Matrices II 373 Explicit Form of the Dirac Matrices 378 Relativistic Invariance of the Dirac Equation 379 Explicit Transformation Matrix 383 Traces of Gamma Matrices 384 Problems 385 Chapter 23: SOLUTIONS OF THE DIRAC EQUATION 387 Free-Particle Solution 387 Physical Interpretation of Dirac Matrices 389 Spin 391 Dirac Equation in External Field 393 Nonrelativistic Limit 395 Exact Solution of Dirac Equation for Coulomb Potential 398 Negative Energy Solutions 404 Perturbation Theory 405 Problems 407 Index 410 A 410 B 410 C 410 D 411 E 411 F 411 G 412 H 412 I 412 J 412 K 412 L 412 M 412 N 413 O 413 P 413 Q 413 R 413 S 413 T 414 V 414 W 414 Z 415 Pt. I. Theory Of Atomic Structure -- Ch. 1. Miscellaneous Results From Elementary Quantum Mechanics -- Ch. 2. Identical Particles And Symmetry -- Ch. 3. Two-electron Atoms -- Ch. 4. Self-consistent Field -- Ch. 5. Statistical Models -- Ch. 6. Addition Of Angular Momenta -- Ch. 7. Theory Of Multiplets, Electrostatic Interaction -- Ch. 8. Theory Of Multiplets, Spin-orbit Interaction, And Interactions With External Fields -- Ch. 9. Molecules -- Pt. Ii. Semiclassical Radiation Theory -- Ch. 10. Semiclassical Theory Of Radiation -- Ch. 11. Intensity Of Radiation, Selection Rules -- Ch. 12. Photoelectric Effect -- Pt. Iii. Atomic Collisions -- Ch. 13. Elastic Scattering At High Energies -- Ch. 14. Elastic Scattering At Low Energies -- Ch. 15. Further Corrections To Elastic Scattering Formulas -- Ch. 16. Elastic Scattering Of Spin 1/2 Particles -- Ch. 17. Inelastic Scattering At High Energies -- Ch. 18. Inelastic Scattering At Low Energies -- Ch. 19. Semiclassical Treatment Of Inelastic Scattering -- Ch. 20. Classical Limit Of Quantum Mechanical Scattering; Summary -- Pt. Iv. Relativistic Equations -- Ch. 21. Klein-gordon Equation -- Ch. 22. Dirac Equation, Formal Theory -- Ch. 23. Solution Of The Dirac Equation. Hans A. Bethe, Roman Jackiw. The Advanced Book Program. Includes Bibliographical References And Index. Graduate students in both theoretical and experimental physics will find this third edition of Intermediate Quantum Mechanics, refined and updated in 1986, indispensable. The first part of the book deals with the theory of atomic structure, while the second and third parts deal with the relativistic wave equations and an introduction to field theory. Throughout its nearly thirty-five years in print, Intermediate Quantum Mechanics has consistently offered more complete coverage of applications of quantum mechanics than any other single-volume work on the subject.