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Durham University

Department of Physics

PHYS4251 Foundations of Physics 4A (2018/19)

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


Quantum Mechanics 3

Dr N. Gidopoulos

14 lectures + 5 workshops in Michaelmas Term


Required: Introduction to Quantum Mechanics, B.H. Bransden and C.J. Joachain (Prentice Hall, 2nd Edition)
The course is defined by material contained in this book and in particular the material defined in the syllabus below where the numbers refer to the sections in the book.

Additional: Introduction to Quantum Mechanics, D. J. Griffiths (2nd edition, Pearson, 2005)
The course is partly defined by material contained in Chapter 6 of this book which has been placed on duo.

Additional: Physics of Atoms and Molecules, B. H. Bransden and C. J. Joachain (2nd edition, Prentice Hall, 2003)
The course is partly defined by material contained in Chapter 7 of this book which has been placed on duo.

Additional: Quantum Mechanics - An Experimentalist's Approach, E. D. Commins (Cambridge University Press, 2014)


  1. Introduction to many-particle systems (wave function for systems of several particles, identical particles, bosons and fermions, Slater determinant) [10.1,10.2]
  2. The variational method (ground state, excited states, trial functions with linear variational parameters) [8.3]
  3. The ground state of two-electron atoms [10.4]
  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]
  5. Complex atoms (electronic shells, the central-field approximation) [10.5]
  6. Time-dependent perturbation theory [9.1]
  7. Fermi’s Golden Rule [9.2]
  8. Periodic perturbations [9.3]
  9. The Schrödinger equation for a charged particle in an EM field [11.1]
  10. The dipole approximation [11.1]
  11. Transition rates for harmonic perturbations [11.2]
  12. Absorption and stimulated emission [11.2]
  13. Einstein coefficients and spontaneous emission [11.3]
  14. Selection rules for electric dipole transitions [11.4]
  15. Lifetimes [11.5]
  16. 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]
  17. One-electron atoms in magnetic fields [12.3, Griffiths 6.4]

Nuclear and Particle Physics

Dr D. Maitre and Dr M. Bauer

29 lectures + 12 workshops in Michaelmas and Epiphany Terms


Required: Particles and Nuclei: An Introduction to the Physical Concepts, B. Povh, K Rith, C. Scholz and C Zetsche (Springer-Verlag, 6th Edition)
The course is defined by material contained in this book, in particular Chapters 1-17.

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 relativistic kinematics 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), deep inelastic scattering (nucleon excited states, structure functions, the parton model), quarks, gluons, and the strong interaction (quark structure of nucleons, quarks in hadrons), particle production in electron-positron collisions (lepton pair production, resonances), phenomenology of the weak interaction (weak interactions, families of quarks and leptons, parity violation), exchange bosons of the weak interaction (real W and Z bosons), 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).


2 or 3 lectures in Easter Term, including one by each lecturer.

Teaching Methods

Lectures: 2 or 3 one hour lectures per week

Workshops: These provide an opportunity to work through and digest the course material by attempting exercises assisted by direct interaction with the workshop leaders. They also provide opportunity for you to obtain further feedback on the self-assessed formative weekly problems. Students will be divided into four groups, each of which will attend one one-hour class every week. The workshops for this module are not compulsory.

Progress test: One compulsory formative progress test (to be completed over the Christmas break)

Problem exercises: See

Dissertation: Students undertake a dissertation in physics of approximately 1500 words in length. The subject matter is to be chosen with the advice of the course lecturers who will provide a list of suitable topics. The aim should be to pick a topic which has a high physics content appropriate for Level 4, which is accessible to the student and can be readily researched, and which can be discussed satisfactorily within the word count limit. The technical level should be advanced, rather than introductory. 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 feedback including the marks awarded for the dissertation) will be returned to students before the end of the Epiphany Term.