#### Prerequisites
* Foundations of Physics 3A (PHYS3621) AND (Theoretical Physics 3 (PHYS3661) OR (Mathematical Physics II (MATH2071) AND Special Relativity and Electromagnetism II (MATH2657))).
#### Corequisites
* Advanced Quantum Theory IV (MATH4061) if Theoretical Physics 3 (PHYS3661) has not been taken.
#### Excluded Combination of Modules
* None.
#### Aims
* 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.
#### Content
* 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).
#### Learning Outcomes
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:
#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
* 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.
More information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4141