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

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Spin-12 particles; neutron interferometry

       1.17 The Bargmann representation

       1.17.1 Representation of operators

       1.18 Coherent states for SU(2)

       1.19 Properties of SU(2) from coherent states

       1.20 Exercises

       References

       2 Addition of angular momenta and spins

       2.1 The coupling of two spin-12 particles

       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)

      

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