AIMS OF THE MODULE:
• To provide the basis for the physical interpretation of quantum mechanics.
• To develop an understanding of advanced topics and techniques in quantum mechanics.
• To develop skills in applying these techniques to problems in solid state and atomic physics.
• To develop a basic understanding of nuclear physics, using quantum mechanical concepts.
• To apply this to nuclear stability and nuclear reactions.

The student will be able to:
• Obtain an understanding of the fundamental postulates of quantum mechanics in the operator formalism and use the Dirac notation in simple cases.
• Derive the orbital magnetic moment of the H atom, show an understanding of the electron spin and explain the Stern-Gerlach experiment.
• Show comprehension of the concepts of generalised angular momentum and the angular momentum addition theorem and apply these concepts to explaining the fine structure in atomic spectra
• Demonstrate application of time-independent  and time-dependent perturbation theory to simple problems.
• Demonstrate an understanding of what causes atoms to radiate, specifically atomic electric dipole radiation and selection rules.
• Describe the properties of the nucleus in terms of fundamental forces and quantum mechanics.
• Describe the models of the nucleus and show how they can be used to understand nuclear stability.
• Give an account of, and be able to apply, the systematics of decay processes and nuclear reactions.

Lectures 33 x 1 hr, Exercises 11 x 1hr.

Problem solving.  Mathematics.  Analytical skills

Examination 80%.  Coursework 20%.  [Examination duration: 3 hours]

• Operator formalism: Eigenstates and eigenvalues. Complete normalized orthogonal sets. Dirac notation.
• Generalized angular momentum: Commutation relations, ladder operators, integer and half-integer spin.
• Two-electron system: Angular momentum addition theorem, multiplets and fine structure in atomic spectra.
• Perturbation theory: introduction to time-independent and time-dependent perturbation methods in quantum mechanics.
• The variational method and its application.
• Applications of the quantum theory to solids, double-well potential (bilayers), tunnelling (scanning tunnelling microscope).
• Application of perturbation theory to electron states in atoms:  dc and ac Stark shift (atomic spectra in electric field), Zeeman effect and Landau-Zener transition, Rabi oscillations (NMR, Josephson junctions) , Landau levels and the Quantum Hall Effect, atomic structure (fine and hyperfine), stimulated and spontaneous transition and Fermi's golden rule (atom-light interaction).  Selection rules.
• Multi-electron atoms: Indistinguishability of particles and the exclusion principle, central field approximation, electronic configuration and the Periodic table.
• The basics of nuclear physics. The deuteron.  Nuclear masses and nuclear sizes.  Isotopes, radioactivity. Fission and fusion
• Simple models of nuclear structure: Droplet model and semi-empirical mass formula. Shell model and magic nuclei.
• Microscopic pictures of nuclear physics:  Nuclear forces. Isospin.  Kinematics of nuclear decays and reaction.  Theories of alpha, beta, and gamma radiation.

Nuclear Physics: Principles and Applications, J Lilly (John Wiley & Sons 2001)
Introductory Nuclear Physics, K S Krane (John Wiley & Sons 1988)
Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, R Eisberg and R Resnick (John Wiley & Sons 1985)