Quantum Mechanics 10 hp / Kvantmekanik 10 hp

Master level course (code 1FA352) for Physics and Engineering Physics (teknisk fysik)

News: Exam with solutions available here: | Exam 2011-12-16 solutions

Introduction

The course runs over the whole fall semester, starting August 29. It is given in English within the Engineering Physics programme (4th year) and Physics Master or other curricula.

Course syllabus / Kursplan

Contents in brief: Advanced non-relativistic quantum mechanics based on the Dirac formalism with bra and ket vectors, operators and observables. Position and momentum space representations. Schrödinger and Heisenberg pictures. The harmonic oscillator with creation and annihilation operators. Operators for translation, time evolution and rotation. Quantisation and addition of angular momenta. Tensor operators. Symmetries and gauge transformations.
Time-independent and time-dependent pertubation theory. Basic scattering theory with applications in different sciences. Interpretation of quantum mechanics with its experimental verification via Bell's inequality and violation against Einstein's local realism and theories with hidden variables. Entangled states. Introduction to quantum technology/information.
Laboratory exercises / miniprojects.

Specification of the course 2011 (pdf 70 kB)

Register for participating in the course via Studentportalen or course secretariat. In case of problems, send e-mail to GI with subject "QM" and 1-line content: personal number (yymmdd-xxxx), last name, first name, e-mail address, study program (T, master, Erasmus, grad.stud., ...)

Teachers:

Gunnar Ingelman (course responsibility), web page, e-mail
Theoretical High Energy Physics group, Division of Nuclear and Particle Physics
Department of Physics and Astronomy

Jonas Fransson web page, e-mail, Division of Materials Theory

lab course teachers/assistants to be specified

Schedule

This 10 hp course consists of 40++ two-hour lectures/lessons, a half-day computer-based lab with numerical calculation of scattering processes (additional exercises/miniprojects under development).

Detailed schedule with what is covered when.

Official schedule from the engineering school (teknisk fysik).

Literature

Main literature and course material:

J.J. Sakurai, J. Napolitano: Modern Quantum Mechanics, second edition
Pearson, ISBN 10: 0-321-50336-8; ISBN 13: 978-0-321-50336-7
This book is a new (sept 2010) second edition (with some new parts added) of the following book which is still fully usable for this course.
[J.J. Sakurai: Modern Quantum Mechanics
Addison-Wesley Publishing Company
ISBN 0-201-53929-2, revised edition 1994]

The parts of Sakurai covered by the course are specified here.

Fundamental concepts and Dirac formalism in Quantum mechanics (pdf 165 kB), lecture notes corresponding to first chapter in Sakurai.

Copies of some lecture material (pdf 2.9 MB)
Answers/solutions to problems (pdf 5.3 MB)

Compendium: Introduction to Collision Theory (to be distributed). Sections 1 to 4 as alternative/complement to chapter 6 [7] in Sakurai.

Overview of scattering theory (pdf 4.2 MB)

Literature for the Bell lab:
Entangled photons, nonlocality, and Bell ... (pdf 0.2 MB)
Entangled photon apparatus ... (pdf 0.3 MB)
Experimental violation of a Bell's inequality ... (pdf 0.2 MB)
Lab instructions:
Bell-lab instruction (pdf 1.2 MB)
Apparatus & schedule (pdf 3.4 MB)
Lab-groups (pdf 0.15 MB)

Literature for the part on "Quantum Information":

Main literature to be specified ...

The original paper on quantum teleportation:
C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993) available here

The original paper on entanglement assisted quantum cryptography:
A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991) available here

Highly recommended lecture notes:
J. Preskill, Quantum Information and Computation available here

Excellent introduction to quantum information and quantum computation:
S. Stenholm and K.-A. Suominen, Quantum approach to informatics (Wiley, New Jersey, 2005)

First monograph on quantum information science:
M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)

Updated review on quantum computer hardware:
T.D. Ladd, F. Jelezko, R. La°amme, Y. Nakamura, C. Monroe, and J.L. O'Brien, Nature 464, 45 (2010)

Other literature for extra reading:

G. Greenstein, A.G. Zajonc: The quantum challenge - Modern research on the foundations of quantum mechanics
Jones And Bartlett Publishers 2006, ISBN 0-7637-2470-X paperback (Bokus 421 SEK)

Where to find books:
Sakurai-Napolitano you can find at the following book stores in Uppsala (prices Aug. 2011):
- at Studentbokhandeln (www.studentbokhandeln.se) for a price of 679 SEK or 611 SEK with 10% discount when buying for more than 1000 SEK (e.g. two students buying together).
- at LundeQ (www.akademibokhandeln.se) for a student-price of xxx SEK

You can also try these internet links:

Uppsala University Library - Search with DISA
Swedish book resources on internet:
Bokfynd: Jämför priser för Sakurai - Modern Quantum Mechanics
Akademibokhandeln
Studentbokhandeln
Bokus
Other resources:
Blackwells
Amazon.co.uk

Problems

The problems to be solved in classes or indicated as individual exercises are from Sakurai and from the problem-collection in the Compendium; see details here (pdf 70 kB)

Computer Lab

The computer lab is on Monday 7 November 13:15 - 17:00 in Ångström 4102, 4103. Participation is mandatory.

This is a computer based study of Quantum Scattering in 3D through numerical computations of a nuclear physics model problem, the scattering of an alpha particle off the nucleus C¹². The numerical calculations are performed using a Quantum Mechanics package written by Bengt Karlsson for MATLAB version 5.3 or higher.

For the dedicated students, who would like to try the qmech package at home, you can download an archive with the files provided at at the lab, the instructions manual and the answers sheet which can be used as a hand-in report.

Downloads:
  - package with program as a tarball or zip archive,
  - instructions manual in PS or PDF format,
  - practical instructions and "Questions and Answers" sheet in PS or PDF format.
  - templates for some of the tasks

Examination / Old exams

The examination will take place on Friday 16 December 2011 at XX.00-YY.00

The written exam take 5 hours and usually consists of solving 6 problems (including theory questions where relevant) from all main areas of the course. The whole exam is usually worth 24 points and the threshold for passing the exam will be around 50%. Aproaching all problems is appreciated and partial credits are given.

The following are allowed as aids:
  - Physics Handbook
  - Mathematics Handbook
  - collection of formulae distributed with the exam
  - calculator