Quantum Mechanics for Nuclear Structure, Volume 2. Professor Kris Heyde

2.2 The general coupling of two particles with spin or angular momentum

       2.3 Spin–orbit coupling

       2.4 Vector spherical harmonics

       2.5 Clebsch–Gordan coefficients and rotation matrices

       2.6 The coupling of many spins and angular momenta and their recoupling

       2.6.1 6-j coefficients

       2.6.2 9-j coefficients

       3 Vector and tensor operators

       3.1 Vector operators

       3.2 Tensor operators

       3.3 Matrix elements of spherical tensor operators and the Wigner–Eckart theorem

       4 Identical particles

       4.1 Slater determinants

       4.2 The occupation number representation for bosons

       4.3 The occupation number representation for fermions

       4.4 Hamiltonians and other operators in the occupation number representation

       4.4.1 Exercises

       4.5 Condensed states (superconductors and superfluids)

       4.5.1 Two fermions in a degenerate set of levels with a pairing force

       4.5.2 Many fermions in a degenerate set of levels with a pairing force: the quasispin formalism

       4.5.3 BCS theory

       4.6 The Lipkin model

       Reference

       5 Group theory and quantum mechanics

       5.1 Definition of a group

       5.2 Groups and transformation

       5.2.1 Translations

       5.2.2 Rotations

       5.2.3 Space–time transformation

       5.3 Transformation on physical systems

       5.4 Quantum mechanics: a synoptic view

       5.5 Symmetry transformations in quantum mechanics

       5.5.1 The unitary transformations for translations, rotations, and time evolution in quantum mechanics

       5.5.2 Consequences of symmetry in quantum mechanics

       5.6 Models with symmetry in quantum mechanics

       5.7 Groups and algebras

       5.8 Dynamical or spectrum generating algebras

       5.9 Matrix groups

       5.9.1 Discrete matrix groups

       5.9.2 Continuous matrix groups

       5.9.3 Compact and non-compact groups

       5.9.4 Polynomial representation of groups

       5.10 Generators of continuous groups and Lie algebras

       5.10.1 The matrix group SO(3) and its generators

       5.10.2 Unitary groups and SU(2)

       5.11 The unitary and orthogonal groups in n dimensions, U(n) and SO(n)

       5.12 Casimir invariants and commuting operators

       5.12.1 The Casimir invariants of u(n)

       5.12.2 The Casimir invariants of so(n)

       6 Algebraic structure of quantum mechanics

       6.1 Angular momentum theory as an application of a Lie algebra

       6.2 The Lie algebra su(1,1) ∼ sp(1,R)

       6.3 Rank-2 Lie algebras

       6.3.1 su(3) and the isotropic harmonic oscillator in three dimensions

       6.3.2 so(4) and the hydrogen atom (Kepler problem)

       6.4 so(5) and models with ‘quadrupole’ degrees of freedom (Bohr model)

       6.5 The Lie algebra sp(3,R) and microscopic models of nuclear collectivity

       6.6 Young tableaux

       6.6.1 SU(3) tensor tableau calculus

       6.6.2 Multiplicity of a weight state in an SU(3) irrep

       6.6.3