Undergraduate Course: Quantum Theory (PHYS11019)

Course Outline
School	School of Physics and Astronomy	College	College of Science and Engineering
Course type	Standard	Availability	Available to all students
Credit level (Normal year taken)	SCQF Level 11 (Year 4 Undergraduate)	Credits	10
Home subject area	Undergraduate (School of Physics and Astronomy)	Other subject area	None
Course website	http://www.ph.ed.ac.uk/~bjp/qt	Taught in Gaelic?	No
Course description	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.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	It is RECOMMENDED that students have passed ( Complex Variable & Differential Equations (MATH10033) OR Complex Variable (MATH10001)) AND Lagrangian Dynamics (PHYS10015) AND Symmetries of Classical Mechanics (PHYS10088)	Co-requisites	It is RECOMMENDED that students also take Quantum Physics (PHYS10043)
Prohibited Combinations		Other requirements	At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule P or Q
Additional Costs	None

Information for Visiting Students
Pre-requisites	None
Displayed in Visiting Students Prospectus?	Yes

Course Delivery Information

Delivery period: 2013/14 Semester 1, Available to all students (SV1)			Learn enabled: Yes	Quota: None
Web Timetable	Web Timetable
Class Delivery Information	Workshop/tutorial sessions, as arranged.
Course Start Date	16/09/2013
Breakdown of 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 )
Additional Notes
Breakdown of Assessment Methods (Further Info)	Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Exam Information
Exam Diet	Paper Name	Hours:Minutes
Main Exam Diet S2 (April/May)	Quantum Theory	2:00

Delivery period: 2013/14 Semester 1, Part-year visiting students only (VV1)			Learn enabled: No	Quota: None
Web Timetable	Web Timetable
Class Delivery Information	Workshop/tutorial sessions, as arranged.
Course Start Date	16/09/2013
Breakdown of 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 )
Additional Notes
Breakdown of Assessment Methods (Further Info)	Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Exam Information
Exam Diet	Paper Name	Hours:Minutes
Main Exam Diet S1 (December)	Quantum Theory (VS1)	2:00

Summary of Intended Learning Outcomes
Upon successful completion of the course, it is expected that students will be able to: (1) Understand the basic principles of quantum mechanics; (2) Understand the path integral representation of quantum mechanics; (3) Understand the operator formulation of quantum mechanics; (4) Understand time dependent perturbation theory in quantum mechanics; (5) Understand how to apply perturbation theory to describe scattering; (6) Understand the form and construction of relativistic wave equations; (7) Appreciate the need for quantum field theory. In all the above 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. It is intended that there will be a two-hour workshop each week.

Assessment Information
Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%

Special Arrangements
None

Additional Information
Academic description	Not entered
Syllabus	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.
Transferable skills	Not entered
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 -- possibly the most comprehensive book on Quantum Theory in existence, and it's available electronically (i.e. free!) from Springer via the University Library website.
Study Abroad	Not entered
Study Pattern	Not entered
Keywords	QuaTh

Contacts
Course organiser	Dr Brian Pendleton Tel: (0131 6)50 5241 Email: b.pendleton@ed.ac.uk	Course secretary	Miss Paula Wilkie Tel: (0131) 668 8403 Email: Paula.Wilkie@ed.ac.uk