PHYS4141: ADVANCED THEORETICAL PHYSICS

• Foundations of Physics 3A (PHYS3621) AND (Theoretical Physics 3 (PHYS3661) OR (Mathematical Physics II (MATH2071) AND Special Relativity and Electromagnetism II (MATH2657))).

• Advanced Quantum Theory IV (MATH4061) if Theoretical Physics 3 (PHYS3661) has not been taken.

• None.

• This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
• It builds on the Level 3 modules Foundations of Physics 3A (PHYS3621) and Theoretical Physics 3 (PHYS3661) and provides a working knowledge of non-relativistic quantum mechanical problems at an advanced level appropriate to Level 4 physics students.

• The syllabus contains:
• Revision of electronic structure and Bloch's theorem, many-body Schrodinger equation, Hartree and Hartree-Fock theories, density functional theory, electron exchange and correlation, modern methods of electronic structure calculation. Phonons in three dimensions, beyond the harmonic approximation. Elementary excitations in solids. Superconductivity: historical overview, Meissner effect, Cooper pairs, the superconducting phase transition, supercurrents, the London and Ginzburg-Landau theories, Josephson effects, BCS theory of superconductivity.
• Quantization of light, creation and annihilation operators, Hamiltonian of the field, number states, coherent states, squeezed states, photon bunching and anti-bunching, density operator, pure states, mixed states, entangled states, decoherence, EPR experiments, applications (quantum cryptography, quantum computing, other applications).

Subject-specific Knowledge:

• Having studied this module students will understand some of the modern theories of electronic structure and vibrational properties of materials including superconductivity.
• They will understand the quantum nature of light.
• They will understand the concepts of entangled states and mixed states and their relevance in experiments.

Subject-specific Skills:

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

Key Skills:

• Teaching will be by lectures and workshops.
• The lectures provide the means to give a concise, focused presentation of the subject matter of the module.
• The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.
• When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.
• Regular problem exercises and workshops 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 mutually convenient times.
• Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.
• The open-book examination will provide the means for students to demonstrate the acqusition of subject knowledge and the development of their problem- solving skills.
• The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

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