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 nonrelativistic point particle, and use it to derive timedependent perturbation theory and the Born series for nonrelativistic 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 HamiltonJacobi 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, AharonovBohm effect, Transition elements, Ehrenfest's Theorem and Zitterbewegung.
Timedependent perturbation theory using path integrals: time ordering and the Dyson series, perturbative scattering theory, the Born series, differential crosssections, the operator formulation, time dependent transitions.
Feynman perturbation theory and Feynman diagrams.
Relativistic quantum theory: the KleinGordon 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 twohour workshop each week.

Information for Visiting Students
Prerequisites  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 2021/22, 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 onetoone discussion in workshops and preexam revision sessions. 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   2:00  

Academic year 2021/22, Partyear 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 onetoone discussion in workshops and preexam 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 longwinded 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 ZinnJustin  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.

Additional Information
Graduate Attributes and Skills 
Not entered 
Additional Class Delivery Information 
Workshop/tutorial sessions, as arranged. 
Keywords  QuaTh 
Contacts
Course organiser  Dr Roger Horsley
Tel: (0131 6)50 6481
Email: rhorsley@ph.ed.ac.uk 
Course secretary  Miss Rachel Ord
Tel:
Email: Rachel.Ord@ed.ac.uk 

