Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics

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