Description
This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.
Chapter
2.4. The Physical Significance of the Quantization of Angular Momentum
2.5. The Eigenvectors of the Angular Momentum Operators J2 and Jz
2.6. The Spin Eigenvectors
2.7. Angular Momentum Eigenfunctions in the Case of Large l
2.8. Time Reversal and the Angular Momentum Operators
CHAPTER 3. The Coupling of Angular Momentum Vectors
3.1. The Addition of Angular Momenta
3.2. Commutation Relations between Components of J1, J2, and J
3.3. Selection Rules for the Matrix Elements of J1 and J2
3.4. The Choice of the Phases of the States w(γj1j2jm)
3.5. The Vector Coupling Coefficients
3.6. Computation of the Vector Coupling Coefficients
3.7. The Wigner 3-j Symbol
3.8. Tabulation of Formulas and Numerical Values for Vector-Coupling Coefficients
3.9. Time Reversal and the Eigenvectors Resulting from Vector Coupling
CHAPTER 4. The Representations of Finite Rotations
4.1. The Transformations of the Angular Momentum Eigenvectors under Finite Rotations
4.2. The Symmetries of the
4.4. Recursion Relations for the
4.6. Integrals Involving the
4.7. The as Angular Momentum Eigen functions
CHAPTER 5. Spherical Tensors and Tensor Operators
5.2. The Tensor Operators in Quantum Mechanics
5.3. Factorization of the Matrix Elements of Tensor Operators (Wigner-Eckart Theorem)
5.4. The Reduced Matrix Elements of a Tensor Operator
5.5. Hermitian Adjoint of Tensor Operators
5.6. Electric Quadrupole Moment of Proton or Electron
5.7. The Gradient Formula
5.8. Expansion of a Plane Wave in Spherical Waves
5.9. Vector Spherical Harmonics
5.10. Spin Spherical Harmonics
5.11. Emission and Absorption of Particles
CHAPTER 6. The Construction of Invariants from the Vector-Coupling Coefficients
6.1. The Recoupling of Three Angular Momenta
6.2. The Properties of the 6-j Symbol
6.3. Numerical Evaluation of the 6-j Symbol
CHAPTER 7. The Evaluation of Matrix Elements in Actual Problems
7.1. Matrix Elements of the Tensor Product of Two Tensor Operators
7.2. Selected Examples from Atomic, Molecular and Nuclear Physics
APPENDIX 1. Theorems Used in Chapter 3
APPENDIX 2. Approximate Expressions for Vector-Coupling Coefficients and 6-j Symbols
Cited References and Bibliography
Angular Momentum in Quantum Mechanics
( Investigations in Physics )
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