Quantum mechanics for nuclear structure. Volume 2, An intermediate level view /

The first volume of Quantum Mechanics for Nuclear Structure introduced the reader to the basic elements that underpin the one-body formulation of quantum mechanics. Volume two follows on from its predecessor by examining topics essential for understanding the many-body formulation. The algebraic str...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Heyde, Kris L. G., 1942- (Autor), Wood, J. L. (John L.), 1941- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2020]
Colección:IOP ebooks. 2020 collection.
IOP series in nuclear spectroscopy and nuclear structure.
Temas:
Quantum theory.
Nuclear structure.
Nuclear physics.
SCIENCE / Physics / Nuclear.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Representation of rotations, angular momentum and spin
  • 1.1. Rotations in (3, R)
  • 1.2. Matrix representations of spin and angular momentum operators
  • 1.3. The Pauli spin matrices
  • 1.4. Matrix representations of rotations in ket space
  • 1.5. Tensor representations for SU(2)
  • 1.6. Tensor representations for SO(3)
  • 1.7. The Schwinger representations for SU(2)
  • 1.8. A spinor function basis for SU(2)
  • 1.9. A spherical harmonic basis for SO(3)
  • 1.10. Spherical harmonics and wave functions
  • 1.11. Spherical harmonics and rotation matrices
  • 1.12. Properties of the rotation matrices
  • 1.13. The rotation of <jm|
  • 1.14. The rotation of the Ylm([theta],[phi])
  • 1.15. Exercises
  • 1.16. Spin-1/2 particles; neutron interferometry
  • 1.17. The Bargmann representation
  • 1.18. Coherent states for SU(2)
  • 1.19. Properties of SU(2) from coherent states
  • 1.20. Exercises
  • 2. Addition of angular momenta and spins
  • 2.1. The coupling of two spin-1/2 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
  • 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
  • 4.5. Condensed states (superconductors and superfluids)
  • 4.6. The Lipkin model
  • 5. Group theory and quantum mechanics
  • 5.1. Definition of a group
  • 5.2. Groups and transformation
  • 5.3. Transformation on physical systems
  • 5.4. Quantum mechanics : a synoptic view
  • 5.5. Symmetry transformations 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
  • 5.10. Generators of continuous groups and Lie algebras
  • 5.11. The unitary and orthogonal groups in n dimensions, U(n) and SO(n)
  • 5.12. Casimir invariants and commuting operators
  • 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
  • 6.4. 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
  • 6.7. Introduction to Cartan theory of Lie algebras
  • 7. Perturbation theory and the variational method
  • 7.1. Time-independent perturbation theory
  • 7.2. Time-independent perturbation theory for systems with degeneracy
  • 7.3. An example of (second-order) degenerate perturbation theory
  • 7.4. Perturbation theory and symmetry
  • 7.5. The variational method
  • 8. Time-dependent perturbation theory
  • 8.1. The interaction picture
  • 8.2. Time-dependent perturbation theory
  • 8.3. Constant perturbations and Fermi's golden rule
  • 9. Electromagnetic fields in quantum mechanics
  • 9.1. The quantization of the electromagnetic field
  • 9.2. The interaction of the electromagnetic field with matter
  • 9.3. The emission and absorption of photons by atoms
  • 10. Epilogue.

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