# FYS4480/9480 – Quantum mechanics for many-particle systems ### Level Master and PhD ### Credits 10 ### Teaching Every autumn ### Examination Every autumn ### Teaching language Norwegian (English on request) ## Course content This course gives an introduction to the quantum mechanics of many-body systems and the computational methods relevant for many-body problems in such diverse areas as atomic, molecular, solid-state and nuclear physics, chemistry and materials science. The topics covered are Feynman diagram rules, microscopic mean-field theories (Hartree-Fock and Kohn-Sham theories, natural orbitals), many-body perturbation theory, large-scale diagonalization methods, coupled-cluster theory, quantum computing algorithms for solving quantum-mechanical many-body problems ## Learning outcome After this course you should : - be able to apply these methods to selected physical systems - have a clear understanding of central many-body methods and their strengths and weaknesses - understand the role of many-body correlations starting from various mean field approaches - be able to use second quantization to develop many-body contributions - be able to develop smaller programs that implement central many-body methods - be able to solve quantum mechanical many-body problems using quantum computing algorithms ## Admission Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme. Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student. If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants. ## Prerequisites Recommended previous knowledge A good background in mathematics is needed. Other recommended courses are: FYS3110 – Quantum Mechanics ## Overlapping courses 10 credits overlap with FYS-KJM4480 – Quantum mechanics for many-particle systems (discontinued) 10 credits overlap with FYS-KJM9480 – Quantum mechanics for many-particle systems (discontinued) 10 credits overlap with FYS9480 – Quantum mechanics for many-particle systems (discontinued) ## Teaching The course is based on four lectures per week and two projects. The lecture sessions include also work on weekly exercises and projects. ## Examination Two project assignments that each is given 30% weight in the final grading (60% together). A final oral exam that is given 40% weight in the final grading of the course. ### Examination support material No examination support material is allowed. ## Language of examination You may write your examination papers in Norwegian, Swedish, Danish or English. ## Grading scale Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system. For PhD students it is only pass/not passed. ### Detailed content - Definition of central quantities like Hamiltonians, basis sets, many-body state functions, Slater determinants and other quantum mechanical operators - Second quantization, creation and annihilation operators for fermions and bosons, Normal ordering, Wick's theorem and Wick's generalized theorem for time-independent operators. Time-dependent operators and Wick's time-dependent theorem. - Representing quantum mechanical operators in second quantization - Diagrammatic representation of operators and contractions - Hartree-Fock equations in second quantization and stability criteria, particle-hole formalism, Thouless' theorem - Full configuration interaction theory - Many-body perturbation theory, time-independent and time-dependent. Feynman-Goldstone diagrams and diagrammatic representation of many-body contributions to the energy and other operators. - Coupled cluster theory, standard and unitary theories - Similarity renormalization group methods and in-medium approaches - Variational and diffusion Monte carlo approaches - Basic quantum computing operations (Jordan-Wigner transformation) for studying quantum-mechanical many-particle systems. - Applications to simplified models and selected systems from nuclear, condensed matter, atomic, molecular and quantum chemistry Lecture notes at https://manybodyphysics.github.io/FYS4480/doc/web/course.html . These will be updated.