Undergraduate Course: Quantum Theory (PHYS11019)

Course Outline
School	School of Physics and Astronomy	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 11 (Year 4 Undergraduate)	Availability	Available to all students
SCQF Credits	10	ECTS Credits	5
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.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Principles of Quantum Mechanics (PHYS10094) OR Quantum Mechanics (PHYS09053) It is RECOMMENDED that students have passed Lagrangian Dynamics (PHYS10015) AND ( Honours Complex Variables (MATH10067) AND Electromagnetism and Relativity (PHYS10093)) OR Methods of Theoretical Physics (PHYS10105)	Co-requisites
Prohibited Combinations		Other requirements	At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule P or Q

Information for Visiting Students
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.
High Demand Course?	Yes

Course Delivery Information

Academic year 2023/24, Available to all students (SV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Supervised Practical/Workshop/Studio Hours 20, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 52 )
Assessment (Further Info)	Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment)	Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%
Feedback	Feedback to students is provided in several ways including one-to-one discussion in workshops and pre-exam revision sessions.
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S2 (April/May)			2:00

Academic year 2023/24, Part-year visiting students only (VV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Supervised Practical/Workshop/Studio Hours 20, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 52 )
Assessment (Further Info)	Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment)	Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%
Feedback	Feedback to students is provided in several ways including one-to-one discussion in workshops and pre-exam revision sessions.
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S1 (December)	Semester 1 Visiting Students Only		2:00

Learning Outcomes
On completion of this course, the student will be able to: Understand the basic principles of quantum mechanics and apply them to solve problems in quantum mechanics. Understand and apply the path integral representation of quantum mechanics. Understand and apply the operator formulation of quantum mechanics. Understand time dependent perturbation theory in quantum mechanics and apply perturbation theory to describe scattering. Understand the form and construction of relativistic wave equations and appreciate the need for quantum field theory.

Reading List
As a stimulating introduction to the course: Lectures on Physics, Volume III, RP Feynman. The course doesn't follow any book in detail, but the following textbooks contain material that is closest to the level of the course: Quantum Mechanics and Path Integrals, RP Feynman and AR Hibbs -- the original text on the subject: rather old and a little long-winded but probably closest to the course. There is a new 'Emended Edition' of Feynman and Hibbs by Daniel Styer (Dover Publications). It contains many corrections to the original, and is much cheaper! Principles of Quantum Mechanics, R Shankar. Modern Quantum Mechanics, JJ Sakurai. See also the second half of the book: Path Integrals in Physics, Volume I: Stochastic Processes and Quantum Mechanics, M Chaichian and A Demichev. More advanced texts: Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, H Kleinert - possibly the most complete of all texts on path integrals, but rather long. Path Integrals in Quantum Mechanics, J Zinn-Justin -- ditto, but somewhat less verbose than Kleinert. Quantum Theory, A Wide Spectrum, EB Manoukian -- one of the most comprehensive books on Quantum Theory in existence, and it's available electronically (i.e. free!) from Springer via the University Library website.