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Semester 1

Quantum Theory (PHYS11019)

Subject

Physics and Astronomy

College

SCE

Credits

10

Normal Year Taken

4

Delivery Session Year

2022/2023

Pre-requisites

Knowledge of quantum mechanics at the level of the University of Edinburgh courses listed above. Some knowledge of Lagrangian dynamics, complex analysis, electromagnetism and special relativity is highly recommended.

Course Summary

In this course we review the fundamental ideas of quantum mechanics, introduce the path integral for a non-relativistic point particle, and use it to derive time-dependent perturbation theory and the Born series for non-relativistic scattering. The course concludes with an introduction to relativistic quantum mechanics and the ideas of quantum field theory.

Course Description

Quantum kinematics: slit experiments, Hilbert space, Dirac notation, complete sets of states, operators and observables, space as a continuum, wave number and momentum. Time evolution: the amplitude for a path, the Feynman path integral, relation to the classical equations of motion and the Hamilton-Jacobi equations.Evaluating the path integral for the free particle and the harmonic oscillator. Derivation of the Schroedinger equation from the path integral. The Schroedinger and Heisenberg pictures for time dependence in quantum mechanics. The transition amplitude as a Green function. Charged particle in an EM field, Aharonov-Bohm effect, Transition elements, Ehrenfest's Theorem and Zitterbewegung.Time-dependent perturbation theory using path integrals: time ordering and the Dyson series, perturbative scattering theory, the Born series, differential cross-sections, the operator formulation, time dependent transitions.Feynman perturbation theory and Feynman diagrams.Relativistic quantum theory: the Klein-Gordon and Dirac equations. Negative energy solutions, spin, necessity for a many particle interpretation. Brief introduction to the basic ideas of quantum field theory.In the stated learning outcomes, the generic word "understand" is used to mean that the student must be able to use what s/he has learned to solve a range of unseen problems. The style and level of difficulty of these problems may be found from solving the examples provided in the course, and by the study of past exam papers. A more complete specification of the material included in the course may be found in the syllabus. There will be a two-hour workshop each week.

Assessment Information

Written Exam 100%, Coursework 0%, Practical Exam 0%

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