Module PHYS4251 : FOUNDATIONS OF PHYSICS 4A

Department: Physics

PHYS4251 : FOUNDATIONS OF PHYSICS 4A

Prerequisites

• Foundations of Physics 2A (PHYS2581) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables (MATH2031)).

Corequisites

• None.

Excluded Combination of Modules

• Foundations of Physics 3A (PHYS3621).

Aims

• This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
• It is designed partly for the benefit of students taking certain MSci Joint Honours degrees and partly for any physics students who undertook their third year abroad and could not match the corresponding learning outcomes at the host institution.
• It builds on the Level 2 modules Foundations of Physics 2A (PHYS2581) and Mathematical Methods in Physics (PHYS2611) by providing courses on Quantum Mechanics and Nuclear and Particle Physics.
• It develops skills in researching a topic at an advanced level and in synthesising and describing advanced concepts in a cogent written form.

Content

• The syllabus contains:
• Quantum Mechanics: Introduction to many-particle systems (wave function for systems of several particles, identical particles, bosons and fermions, Slater determinant); the variational method (ground state, excited states, trial functions with linear variational parameters); the ground state of two-electron atoms; the excited states of two-electron atoms (singlet and triplet states, exchange splitting, exchange interaction written in terms of spin operators); complex atoms (electronic shells, the central-field approximation); the Born-Oppenheimer approximation and the structure of the hydrogen molecular ion, vibrational motion, the rigid rotator and rotational energy levels of molecules; the van der Waals interaction; time-dependent perturbation theory; Fermi’s Golden Rule (applications: photoionization, the dielectric function of semiconductors); periodic perturbations; two-level systems with harmonic perturbation, Rabi flopping; the sudden approximation; the Schrödinger equation for a charged particle in an electromagnetic field; the dipole approximation; transition rates for harmonic perturbations; absorption and stimulated emission; Einstein coefficients; spontaneous emission; quantum jumps; selection rules for electric dipole transitions; lifetimes, line intensities, widths and shapes; the ammonia maser and lasers; 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); one-electron atoms in magnetic fields (the Zeeman effect from strong field to weak field, calculation of the Landé g-factor); magnetic resonance.
• Nuclear and Particle Physics: 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).

Learning Outcomes

• Having studied this module students will be familiar with some of the key results of quantum mechanics including perturbation theory and its application to atomic physics and the interaction of atoms with light.
• They will be able to describe the properties of nuclei and how nucleons interact and have an appreciation of the key ingredients of the Standard Model of particle physics.

• In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.
• They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.

• Students will have developed skills in researching a topic at an advanced level and will be able to synthesise and describe advanced concepts in a cogent written form.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Teaching will be by lectures and example classes.
• The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links on DUO.
• Regular problem exercises and example classes will give students the chance to develop their theoretical understanding and problem solving skills.
• Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.
• Lecturers will provide a list of advanced topics related to the module content. Students will be required to research one of these topics in depth and to answer an essay-style examination question on it. Some guidance on the research will be provided by the lecturer.
• Student performance will be summatively assessed through an examination, problem exercises and an open-book conceptual test. The examination and problem exercises will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The open-book conceptual test will provide the means for students to demonstrate skills in researching a topic at an advanced level and describing advanced concepts in a cogent written form.
• The problem exercises and example classes provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Examples classes and problems solved therein.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University