Angular momentum : understanding spatial aspects in chemistry and physics : [the George Fisher Baker non-resident lectureship in chemistry at Cornell University

Designed as a learning tool for those with limited background in quantum mechanics, this book provides comprehensive coverage of angular momentum in quantum mechanics and its applications to chemistry and physics. Based on class-tested material, this presentation offers clear explanations of theory while giving equal attention to solving real problems. Theoretical considerations are made concrete and accessible through extensive examples and applications at the end of each chapter. Problem sets, designed as both individual and group exercises, are treated as an integral part of the text in order to stimulate student interest and clarify the abstract principles discussed. Examples are drawn primarily from atomic and molecular phenomena, and include many intermediate steps (often left out of other texts) to ensure complete mastery of the material, and to lay the groundwork for understanding photon and particle collision phenomena, and more advanced studies. Angular Momentum Preface Contents 1. Angular momentum operators and wave functions 1.1 Definition of angular momentum operators 1.2 Eigenvalues and matrix elements of angular momentum operators 1.3 Angular momentum wave functions 1.4 The vector model Problem set 1 Application 1 Scattering theory 2. Coupling of two angular momentum vectors 2.1 Clebsch-Gordan coefficients 2.2 Clebsch-Gordan coefficients and 3-j symbols: Symmetry properties and explicit values 2.3 Clebsch-Gordan coefficients and 3-j symbols: Geometric interpretation Application 2 The Wigner-Witmer rules Application 3 The rotational energy levels of a doublet Sigma free radical 3. Transformation under rotation 3.1 Angular momentum operators as generators of infinitesimal rotations 3.2 Parameterization of rotations by Euler angles 3.3. The direction cosine matrix elements 3.4 Representation of the angular momentum operators in the space-fixed and molecule-fixed frames 3.5 The rotation matrices 3.6 The rotation matrices: Geometrical interpretation 3.7 The spherical harmonic addition theorem 3.8 The Clebsch-Gordan series and its inverse 3.9 Integrals over products of rotation matrices 3.10 The rotation matrices as rigid body rotational wave functions Application 4 Energy levels of atoms with two valence electrons Application 5 Angular distribution of rigid rotor axes following absorption of plane polarized light Application 6 Photofragment angular distribution (classical treatment) Application 7 Introduction to symmetric tops Application 8 Polarized resonance fluorescence and polarized Raman scattering: Classical expressions Application 9 Magnetic depolarization of resonance fluorescence: Zeeman quantum beats and the Hanle effect Application 10 Correlation functions in molecular spectroscopy 4 Coupling of more than two angular momentum vectors 4.1 The 6-j and 9-j symbols 4.2 Graphical methods Problem set 2 5. Spherical tensor operators 5.1 Definition 5.2 The Wigner-Eckart theorem 5.3 Spherical tensor products 5.4 Tensor product matrix elements Problem set 3 Application 11 The energy levels of a two-valence-electron atom revisited Application 12 Directional correlations; breakup of a long-lived complex Application 13 Orientation and alignment Application 14 Nuclear quadrupole interactions 6. Energy-level structure and wave functions of a rigid rotor 6.1 Moments of inertia: Classification of rigid rotors by top types 6.2 Classical motion of a free top 6.3 Symmetric and asymmetric top energy levels 6.4 Nonrigid behavior: The Van Vleck transformation 6.5 Line strength factors Problem set 4 Application 15 Introduction to diatomic molecules Application 16 Molecular reorientation in liquids Appendix Computer programs for 3-j, 6-j, and 9-j symbols Index Rotational cartoon 7. Errata to 2nd printing of Angular Momentum