# PHYS4251 Foundations of Physics 4A (2013/14)

Details of the module's prerequisites, learning outcomes, assessment and contact hours are given in the official module description in the Faculty Handbook - follow the link above. A detailed description of the module's content is given below, together with book lists and a link to the current library catalogue entries. For an explanation of the library's categorisation system see http://www.dur.ac.uk/physics/students/library/.

## Content

### Quantum Mechanics 3

18 lectures + 4 examples classes in Michaelmas Term

*Textbooks:*

*Syllabus:*

- Introduction to many-particle systems (wave function for systems of several particles, identical particles, bosons and fermions, Slater determinant) [10.1,10.2]
- The variational method (ground state, excited states, trial functions with linear variational parameters) [8.3]
- The ground state of two-electron atoms [10.4]
- The excited states of two-electron atoms (singlet and triplet states, exchange splitting, exchange interaction written in terms of spin operators) [“Atoms and Molecules”, Ch. 7]
- Complex atoms (electronic shells, the central-field approximation) [10.5]
- The Born-Oppenheimer approximation and the structure of the hydrogen molecular ion; vibrational motion [10.6]
- The rigid rotator and rotational energy levels of molecules [6.4, 10.6]
- The van der Waals interaction [16.1]
- Time-dependent perturbation theory [9.1]
- Fermi’s Golden Rule [9.2] (applications: photoionization [part of 11.7], the dielectric function of semiconductors [e.g., “Fundamentals of Semiconductors”, by Yu and Cardona)
- Periodic perturbations [9.3]
- Two-level systems with harmonic perturbation, Rabi flopping [9.3]
- The sudden approximation [9.5]
- The Schrödinger equation for a charged particle in an EM field [11.1]
- The dipole approximation [11.1]
- Transition rates for harmonic perturbations [11.2]
- Absorption and stimulated emission [11.2]
- Einstein coefficients and spontaneous emission [11.3]
- Quantum jumps [17.5]
- Selection rules for electric dipole transitions [11.4]
- Lifetimes, line intensities, widths and shapes [11.5]
- The ammonia maser and lasers [16.3]
- The interaction of particles with a static magnetic field (spin and magnetic moment, particle of spin one-half in a uniform magnetic field, charged particles with uniform magnetic fields; Larmor frequency; Landau levels) [12.2]
- One-electron atoms in magnetic fields (the Zeeman effect from strong field to weak field, calculation of the Landé g-factor) [12.3, Griffiths 6.4]
- Magnetic resonance [12.4]

### Nuclear and Particle Physics

30 lectures + 6 examples classes in Michaelmas and Epiphany Term

*Textbooks:*

*Syllabus:* Fundamental Interactions, symmetries and conservation Laws, global properties of nuclei (nuclides, binding energies, semi-empirical mass formula, the liquid drop model, charge independence and isospin), nuclear stability and decay (beta-decay, alpha-decay, nuclear fission, decay of excited states), scattering (elastic and inelastic scattering, cross sections, Fermi's golden rule, Feynman diagrams), geometric shapes of nuclei (kinematics, Rutherford cross section, Mott cross section, nuclear form factors), elastic scattering off nucleons (nucleon form factors, quasi elastic scattering), deep inelastic scattering (nucleon excited states, structure functions, the parton model), quarks, gluons, and the strong interaction (quark structure of nucleons, quarks in hadrons, the quark-gluon interaction, scaling violations), particle production in electron-positron collisions (lepton pair production, resonances, gluon emission), phenomenology of the weak interaction (weak interactions, families of quarks and leptons, parity violation, deep inelastic neutrino scattering), exchange bosons of the weak interaction (real W and Z bosons, electroweak unification), the Standard Model, quarkonia (analogy with Hydrogen atom and positronium, Charmonium, quark-antiquark potential), hadrons made from light quarks (mesonic multiplets, baryonic multiplets, masses and decays), the nuclear force (nucleon-nucleon scattering, the deuteron, the nuclear force), the structure of nuclei (Fermi gas model, shell Model, predictions of the shell model).

### Revision

2 Lectures in Easter Term, one by each lecturer.

## Teaching Methods

*Lectures:* 2 or 3 one hour lectures per week

*Examples classes:* These provide an opportunity to work through and digest the course material by attempting exercises and assignments assisted by direct interaction with the lecturers and demonstrators. Students will be divided into groups, each of which will attend one one-hour class every fortnight.

*Dissertation:*Students undertake a dissertation in Physics of approximately 3000 words in length.

Students should discuss with the lecturer the qualities expected in the dissertation, but an indication of these is given in the mark proforma used for assessment. The proforma will be made available to students for their information at the beginning of the Michaelmas Term. The dissertation is summatively assessed.

The marked dissertations along with the completed proformas (giving the marks awarded for the dissertation) will be returned to students before the end of the Epiphany Term.

*Problem exercises:* See http://www.dur.ac.uk/physics/students/problems/