TY - BOOK AU - Burkhardt, Charles. AU - Leventhal, Jacob J. TI - Topiczs in atomic physics SN - 9780387257488 U1 - 539.7 PY - 2006/// CY - New York PB - Springer KW - Nuclear physics KW - Atomic theory KW - Molecular structure KW - Physics KW - Quantum theory N1 - Chapter 1 Background......................................... 1 1.1 Introduction .............................. . ...... ............ ........... .. 1 1.2 The Bohr Model of the Atom ............................................... 1 1.3 Numerical Values and the Fine Structure Constant..................... 7 1.4 Atomic Dimensions-Is ao a Reasonable Atomic Diameter?......... 8 1.5 Localizing the Electron: Is a Point Particle Reasonable? ............ 10 1.6 The Classical Radius of the Electron...................................... 11 1.7 Atomic Units ................... ...... ................... .......... ..... . 11 Chapter 2 Angular Momentum................................ 14 2.1 Introduction ................................................................. .. 14 2.2 Commutators................................................................... 18 2.3 Angular Momentum Raising and Lowering Operators ............... 20 2.4 Angular Momentum Commutation Relations with Vector Operators .............................................................. 25 2.5 Matrix Elements of Vector Operators ..................................... 26 2.6 Eigenfunctions of Orbital Angular Momentum Operators ............. 29 2.7 Spin ............................................ ................... ............. . 33 2.8 The Stern-Gerlach Experiment........................................ 41 Chapter 3 Angular Momentum-Two Sources.............. 46 3.1 Introduction ................................................ .................... 46 3.2 Two Sets of Quantum Numbers-Uncoupled and Coupled.......... 46 3.3 Vector Model of Angular Momentum.................................. 51 3.4 Examples of Calculation of the Clebsch-Gordan Coefficients....... 55 3.5 Hyperfine Splitting in the Hydrogen Atom.............................. 61 Chapter 4 The Quantum Mechanical Hydrogen Atom.... 73 4.1 The Radial Equation for a Central Potential ............................. 73 4.2 Solution of the Radial Equation in Spherical Coordinates-The Energy Eigenvalues................................. 75 4.3 The Accidental Degeneracy of the Hydrogen Atom.................... 77 4.4 Solution of the Hydrogen Atom Radial Equation in Spherical Coordinates-The Energy Eigenfunctions................... 79 4.5 The Nature of the Spherical Eigenfunctions........................... 82 4.6 Separation of the Schr6dinger Equation in Parabolic Coordinates....................................................... 82 4.7 Solution of the Separated Equations in Parabolic Coordinates-The Energy Eigenvalues................................. 85 4.8 Solution of the Separated Equations in Parabolic Coordinates-The Energy Eigenfunctions............................. 87 Chapter 5 The Classical Hydrogen Atom................... 92 5.1 Introduction .......................... ................... ....... ............... 92 5.2 The Classical Degeneracy ................................................... 95 5.3 Another Constant of the Motion-The Lenz Vector.................... 97 Chapter 6 The Lenz Vector and the Accidental Degeneracy......... .................................. 105 6.1 The Lenz Vector in Quantum Mechanics................................ 105 6.2 Lenz Vector Ladder Operators; Conversion of a Spherical Eigenfunction into Another Spherical Eigenfunction.................. 109 6.3 Application of Lenz Vector Ladder Operators to a General Spherical Eigenfunction.................. ....................... 114 6.4 A New Set of Angular Momentum Operators............................ 116 6.5 Energy Eigenvalues....................................................... ... 118 6.6 Relations Between the Parabolic Quantum Numbers ................ 120 6.7 Relationship Between the Spherical and Parabolic Eigenfunctions............... .................................. . 122 6.8 Additional Symmetry Considerations................................... 123 Chapter 7 Breaking the Accidental Degeneracy ......... 126 7.1 Introduction ................. ..................... ................. ......... 126 7.2 Relativistic Correction for the Electronic Kinetic Energy .............. 127 7.3 Spin-Orbit Correction...................................................... 128 7.4 The Darwin Term ............................................................ 130 7.5 Evaluation of the Terms That Contribute to the Fine-Structure of Hydrogen ..... .............................. . ... ..................... 130 7.6 The Total Fine-Structure Correction....................................... 135 7.7 The Lamb Shift............................................................... 137 7.8 Hyperfine Structure........................................................... 139 7.9 The Solution of the Dirac Equation........................................ 142 Chapter 8 The Hydrogen Atom in External Fields......... 145 8.1 Introduction ................. ...... ................. .......... ............... 145 8.2 The Zeeman Effect-The Hydrogen Atom in a Constant Magnetic Field................................................................. 146 8.3 Weak Electric Field-The Quantum Mechanical Stark Effect ........ 159 8.4 Weak Electric Field-The Classical Stark Effect....................... 171 Chapter 9 The Helium Atom ........... ................ ......... 178 9.1 Indistinguishable Particles................................................... 178 9.2 The Total Energy of the Helium Atom.................................... 180 9.3 Evaluation of the Ground State Energy of the Helium Atom Using Perturbation Theory .............................. ..... .......... 183 9.4 The Variational Method.................................................... 186 9.5 Application of the Variational Principle to the Ground State of Helium ................................................................ 187 9.6 Excited States of Helium................................................. 189 9.7 Doubly Excited States of Helium: Autoionization...................... 192 Chapter 10 Multielectron Atoms................................ 196 10.1 Introduction .......................... ....... ......... ..... ... ............. ... 196 10.2 Electron Configuration....................................................... 196 10.3 The Designation of States-LS Coupling ................................ 198 10.4 The Designation of States-jj Coupling................................ 207 Chapter 11 The Quantum Defect ............................... 214 11.1 Introduction ............................... ....... .. ....... ... ................... 214 11.2 Evaluation of the Quantum Defect........................................ 216 11.3 Classical Formulation of the Quantum Defect and the Correspondence Principle.................................................. 220 11.4 The Connection Between the Quantum Defect and the Radial Wave Function....................................................... 225 Chapter 12 Multielectron Atoms in External Fields....... 230 12.1 The Stark Effect.............................................................. 230 12.2 The Zeeman Effect.......................................................... 238 Chapter 13 Interaction of Atoms with Radiation......... 246 13.1 Introduction ............................. .. ........ ..... ....... ............... 246 13.2 Time Dependence of the Wave Function............................... 248 13.3 Interaction of an Atom with a Sinusoidal Electrom agnetic Field........................................................ 249 13.4 A Two-State System-The Rotating Wave Approximation............ 251 13.5 Stimulated Absorption and Stimulated Emission ...................... 254 13.6 Spontaneous Emission ....................................................... 260 13.7 Angular Momentum Selection Rules..................................... 266 13.8 Selection Rules for Hydrogen Atoms ................................... 267 13.9 Transitions in Multielectron Atoms........................................ 272 Answers to Selected Problems............................................ 279 ER -