Quantum mechanics for nuclear structure. a primer / Volume 1 :

This book, the first of a two-volume set, provides a comprehensive introduction to quantum mechanics for advanced undergraduate and postgraduate students entering the field of nuclear structure studies via two-state systems: both polarized photons and spin-1/2 particles. This leads to the logic behi...

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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. A theory of polarized photons
  • 1.1. Polarized lightwaves
  • 1.2. Polarized photons
  • 1.3. Uncertainty in experiments
  • 1.4. Dirac bracket notation
  • 1.5. Transformation properties of polarizing filter measurements
  • 1.6. Multiples of kets
  • 1.7. Exercises
  • 2. A theory of the Stern-Gerlach experiment for spin-1-2 particles
  • 2.1. The Stern-Gerlach experiment
  • 2.2. Sequences of Stern-Gerlach measurements
  • 2.3. State representation for spin-1-2 particles
  • 2.4. The choice of basis kets
  • 2.5. Exercises
  • 2.6. An introduction to operators for spin-1-2 particles
  • 2.7. Exercises
  • 3. The axioms of quantum mechanics
  • 3.1. Global axioms of observation
  • 3.2. Axioms for quantum mechanical observations
  • 3.3. Axioms for the mathematical structure of quantum mechanics
  • 3.4. Axioms for the incorporation of h in quantum mechanics
  • 3.5. Exercise
  • 4. Linear spaces and linear operators
  • 4.1. Definitions and theorems for linear spaces and linear operators
  • 4.2. Linear spaces, Dirac bras and kets, and operators
  • 4.3. Outer products of Dirac bras and kets
  • 4.4. Exercises
  • 5. The harmonic oscillator
  • 5.1. The quantum mechanical one-dimensional harmonic oscillator
  • 5.2. The quantum mechanical two-dimensional harmonic oscillator
  • 5.3. Time dependence of the one-dimensional quantum harmonic oscillator
  • 5.4. Exercises
  • 5.5. Coherent states and the one-dimensional harmonic oscillator
  • 6. Representations : matrices
  • 6.1. Basics of matrix manipulation
  • 6.2. Exercises
  • 6.3. The two-level mixing problem
  • 6.4. Exercises
  • 6.5. Unitary transformations and matrix diagonalization
  • 6.6. Exercises
  • 6.7. Matrix diagonalization : the Jacobi method
  • 6.8. Exercise
  • 7. Observables and measurements
  • 7.1. Basic concepts
  • 7.2. The uncertainty relation
  • 7.3. Exercises
  • 7.4. Mixtures and the density matrix
  • 8. Representations : position, momentum, wave functions, and function spaces
  • 8.1. The concept of a wave function
  • 8.2. The quantum mechanical structure of position and momentum
  • 8.3. The wave-like properties of matter
  • 8.4. Exercises
  • 9. Quantum dynamics : time evolution and the Schrödinger and Heisenberg pictures
  • 9.1. Basic relations
  • 9.2. Spin precession
  • 9.3. Exercises
  • 9.4. Correlation amplitude and the energy-time uncertainty relation
  • 9.5. The Schrödinger and Heisenberg pictures
  • 9.6. The free particle in the Heisenberg picture
  • 9.7. Schrödinger's wave equation
  • 9.8. Exercises
  • 9.9. Alternative derivation of the energy-time uncertainty relation
  • 9.10. Time-dependent phenomena
  • 9.11. Time-dependent two-state problems
  • 9.12. Exercise
  • 10. Rotations and continuous transformation groups
  • 10.1. Elements of group theory
  • 10.2. Matrix groups
  • 10.3. Exercises
  • 10.4. Rotations in physical space
  • 10.5. Exercise
  • 10.6. Rotations of quantum mechanical states
  • 10.7. Exercise
  • 11. Angular momentum and spin in quantum mechanics
  • 11.1. The algebra of angular momentum in quantum mechanics
  • 11.2. Algebraic solution of the quantum mechanical angular momentum problem
  • 11.3. Exercises
  • 12. Central force problems
  • 12.1. General features of central force problems
  • 12.2. Central force problems, factorization algebra and isospectral Hamiltonians
  • 12.3. The hydrogen atom central force problem
  • 12.4. The three-dimensional isotropic harmonic oscillator central force problem
  • 12.5. The three-dimensional isotropic infinite square well central force problem
  • 12.6. Exercises
  • 12.7. Central force problems and so(2, 1) or su(1, 1) algebra
  • 12.8. so(2, 1) solution for the hydrogen atom
  • 12.9. so(2, 1) solution for the three-dimensional isotropic harmonic oscillator
  • 13. Motion of an electron in a uniform magnetic field
  • 13.1. Maxwell's equations
  • 13.2. The Landau level problem
  • 13.3. Time dependence of the Landau problem
  • 13.4. Exercises
  • Appendices. A. Commutator bracket relations for central force problems
  • B. Radial wave functions for the hydrogen atom and the three-dimensional isotropic harmonic oscillator.

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