Theoretical Physics
Chalmers | Göteborg University
QUANTUM MECHANICS FKA081/FYN190
for IMP(F)/F4/GU fall
2003 (5p)
please see
http://fy.chalmers.se/~ostlund/kvant2004.html
GENERAL
INFORMATION
NEWS!
SCHEDULE
LOG
BOOK
EXAMINATION
PROJECT
RELATED MATERIAL
OLD EXAMS
GENERAL INFORMATION
Lectures and examination
Henrik Johannesson, O7104A,
Origo, tel.:
7723185, e-mail: johannesson@fy.chalmers.se
Recitations
Andreas
Käck, D619, MC2, tel.: 7728031, e-mail: and@fy.chalmers.se
Henric Larsson,
O6104B, Origo, tel.: 7723184, e-mail:
solo@fy.chalmers.se
Aim of the course
The course aims at giving a firm
grounding in
non-relativistic quantum mechanics, providing the necessary
background for
basic and applied research in physics
as well as for ``quantum
engineering'' for advanced technologies. The course is built upon
an axiomatic
approach,
exploiting the mathematical theory of linear vector spaces, and
from there on
develops the theory systematically with a large number of
representative
examples, including some of the most recent developments in
quantum information,
non-demolition experiments, and the physics of quantum phase
transitions.
Content of the course
Review of fundamental
concepts of quantum
mechanics. Connections with classical physics. The
Schrödinger equation.
Second quantization and the harmonic oscillator. Angular momenta
and spin.
Bell's inequality. Symmetries. Static and time-dependent
perturbations. Quantum
statistics and many-particle systems. Scattering
theory. Geometrical phases. Quantum information.
Text:
J. Sakurai, Modern Quantum Mechanics
Addison-Wesley, 1994. The book can be bought at the campus
book store.
Supplementary course material can be printed from the course home page.
NEWS!
The course home page is being updated on a
regular basis.
Please make it a
habit to check it out once a week!
For the latest version, click on "Reload".
The "make-up" exam is scheduled for Saturday January 17,
8.45 - 13.45, in "M-huset".
For more information about the exam, please
click here .
Pictures from the Planck Fest!
My lecture notes on time-dependent perturbation theory are avialable here!
The updated schedule for the oral exams is avialable here.
Please note a slight change in the schedule for Friday morning (19/12)!
Also please note that the Monday and Friday orals will take place in FL74.
Due to administrative changes (rules for reporting grades, etc.) I have to move the deadline for submitting the Planck fest written report to Friday January 9.
My SYMMETRY transparencies are available here.
Some practical information about the Planck Fest, scheduled for
Friday December 12, 10.00-12.00 in GD-foajen:
The session starts at 10.00 a.m. sharp; please allow for 15 minutes to
put up your poster! Since this year there is a record number of 22 project groups
I won't be able to check out all posters during the public part of the session (10-12).
If you wish to leave at 12 a.m., please either put up your poster earlier (I will be in
GD-foajen at 9 a.m.), or else arrange with me for a discussion later in the afternoon.
Please prepare a 5-min oral presentation of your work (shared between the project members)
and I will alott another 5 min (roughly) for questions.
The poster screens are 150x120cm (=max size of your poster).
Paper and pins will be available in GD foajen from Wednesday 10/12.
If you need additional material
(colored pens, glue, etc.) please let me know, and I'll try to make it available in my office.
Please don't overdo the project!
Keep it simple and at a popular level!
If you are hard pressed with your other exams, etc. the last week of the semester
it is OK to hand in the written report in January (deadline Jan 15).
For more detailed information, please go to PROJECT.
HP9 is now online!
SCHEDULE
All Tuesday lectures in reading period I are in lecture hall EA ("Elektrohuset").
Time and place for
additional lectures will be announced.
The plan below is tentative only , and will be
updated during
the course.
Please check out the home page on a regular basis!
The recitations are conducted in two groups: FL62 (FL73 in
reading period II), Origo
(English
spoken!) and FL72, Origo (Swedish).
L = Lecture
R = Recitation
S = Support hour* (regularly scheduled
tutoring)
RP = Recommended problems (some of which will be
discussed in the
recitation the nextcoming week). Problems marked with an asterisk
will be solved "interactively" in the recitation. To learn the
material, and also, to benefit optimally from the recitations, it
is crucial that you make an effort to work through as many as
possible of the recommended problems in advance! Also note
that one or two
of the recommended problems will appear on the midterm exam.
HP = Home work problems. To count for the
grade on the course these must
be handed in at the given due date.
* You can also make an appointment with anyone of us
for individual tutoring: Let us know what you need help with
and
we'll try to find a time when we can meet.
|
week 36
L1
L2 |
Historical background
. Some key concepts. What's wrong with classical physics? The double-slit
experiment. Mathematical formalism: linear vector spaces and the Dirac notation.
The postulates of non-relativistic quantum mechanics.
Hilbert spaces. The recitation this week is replaced by an extra lecture. |
Sakurai Ch. 1.1-1.6
RP1
HP1 |
|
week 37
R1 |
No lecture this week. | Sakurai Ch. 1.7
Read the article:
RP2
HP2 |
|
week 38
S1
L3
R2 |
More about Hilbert spaces and the postulates of quantum mechanics. Wave functions in momentum and position space. Measurements, observables, and the uncertainty relation. | Sakurai Ch. 2.1, 2.2, 2.4
RP3
HP3 |
|
week 39
S2
L4
R3 |
The measurement problem. Time evolution: propagators and transition amplitudes. Schrödinger vs. Heisenberg picture. "The most important problem in quantum physics": The harmonic oscillator. | Sakurai Ch. 2.3, 2.5 (p 109-117)
Read the article:
RP4
HP4 |
|
week 40
S3
L5
R4 |
Time evolution and "pictures". More about the harmonic oscillator.
|
Sakurai Ch. 2.5 (p 117 - 123)
RP5
HP5 |
|
week 41
S4
L6
R5 |
Theory of angular momentum. "Classical" and "quantum" rotations.
The angular
momentum commutation relations. The eigenvalue problem of
Lz and L2.
|
Sakurai 2.6, 3.1 - 3.3 (skip the section on Euler angles), 3.5 (p. 187-192), 3.6 (skip the section on "Spherical Harmonics as Rotation Matrices")
RP6
HP6 |
|
week 42
S5
L7
R6 |
Angular momentum eigenfunctions in the coordinate basis.
Spin and multicomponent wave
functions. Spin dynamics.
|
RP7 selected exam problems from 2000-01: Dec 12, 2000: 1 Jan 15, 2001: 1, 3 Oct 30, 2001: 1, 2, 5 Jan 18, 2002: 1, 3, 5 No homework assignment this week. |
|
week 43
R7 prep meeting
Midterm exam
|
A regular five hour midterm exam with both calculations and conceptual essay questions. No book will be allowed. At least one problem will be taken from RP1 - RP7. | |
|
week 44
L8
R8 |
More about angular momentum. Addition of angular momenta. Clebsch-Gordan coefficients. Wigner-Eckart theorem. | Sakurai 3.7, 3.10*. Also please repeat the relevant sections of Sakurai 3.1-3.3, 3.5, 3.6 *optional (those of you continuing with studies in theoretical physics, however, should study this section carefully!)
RP8
|
|
week 45
S6
L9
L10
|
Path integrals. Potentials and gauge transformations. Many-particle systems. Please note that this week's recitation is replaced by an extra lecture.
|
Sakurai Ch. 2.6, 3.9, 6.1-6.4; review 2.5 (117 - 123).
RP9
HP7 |
|
week 46
S7
L11
R9 |
Identical particles and quantum statistics. Quantum entanglement. | Sakurai Ch. 3.9 Read the article: "Physicists Triumph at Guess My Number" by Andrew M. Steane and Wim van Dam, Physics Today, February 2000
RP10
HP8 |
|
week 47
S8
L12
|
Bell's inequalities.
Quantum teleportation.
Mixed states and density matrices. Introduction to symmetries in quantum mechanics. |
Sakurai Ch. 3.4, 4.1
RP11 Read the articles:
"The Copenhagen Interpretation"
"100 years of Quantum Mysteries"
no home work this week |
|
week 48
S9
L13
R11 |
Symmetries and conservation laws.
Translational invariance and
lattices.
Parity. Time-reversal symmetry.
|
Sakurai Ch. 4.2-4.4* *skip the details on p 277-282 (however, you should know the key results: eq. (4.4.72) + Kramers degeneracy)
RP12
HP9 |
|
week 49
R11
S10
L14
L15
|
Perturbation theory. Please note: This week's Thurday recitation is replaced by an extra lecture. |
Sakurai 5.1, 5.2, 5.4-5.6
RP13
|
|
week 50
L16
Review session:
R12
Planck Fest
|
Wrapping up perturbation theory: Interaction picture, Feynman diagrams, and all that...
Elements of scattering theory.
|
|
|
Oral exams
|
LOG BOOK
What happened at the
lectures?
EXAMINATION
The final grade on the course will be based on the following:
GRADES: Masters/F4 students: 40p --> 3,
60p --> 4 80p --> 5
GU students: 40p --> G, 70p --> VG
Ph.D. students: 60p --> Pass
PROJECT
Guide lines:
The PROJECT (to be carried out in groups of 2-3 students) is an optional part of the course, but can add another 15p to your total score (to be counted towards your final grade). The task is to read up on a current topic in Physics, with emphasis on the quantum mechanics component,and to present what you learned in a poster session (to be scheduled some time in December). In addition you should prepare an HTML or postscript/pdf file containing a written report (max 10 pages!) on the subject you’ve studied (to be linked to the course home page for future use in the course). Make sure to include a complete reference list in the report!
For a list of possible topics, including references to an introductory article for each topic and the name of a faculty member / graduate student that you can contact for further advice, please click here. However, you don't have to use my list: please feel free to come up with a topic of your own choice!
The bulk of the poster and the written report should be aimed at a ”popular level”, intelligible to someone with only a passing knowledge of quantum physics. Imagine that you’re writing an article for ”Scientific American”! This will roughly get you at the right level. If possible we will invite the first-year undergraduate physics majors to attend the poster session. Be prepared to explain what you’ve learned to people who are slightly less sophisticated than you are!
If you click here, you’ll find a form which you can copy and fill out once you’ve decided which are your three top choices of topics. If you already know with whom you would like to work, please also list the name(s) of your potential collaborator(s), or else I’ll be the match maker. You can e-mail the form to me or print it out and hand it in to me in at your earliest convenience. One group / topic --> the sooner I get to know your choices, the greater is your chance to get to do what you want to do! As soon as I’ve given you an OK (via e-mail), you’re ready to GO!
Finally: please keep the project work at a reasonable level. Don’t overdo it! You should spend most of your time on the course working with Sakurai and solving as many problems as you find time for - on your own, and together with your fellow students. The PROJECT is no substitute for learning quantum mechanics the hard way! (Besides, it only counts for at most 15p, which is less than half of the maximum total score you can get on the home work assignments). On the other hand, by doing the project you may pick up a fresh perspective on the subject, and also - hopefully - have some fun!
GOOD LUCK!
RELATED MATERIAL
Supplementary reading
Some links
Suggestions and answers to selected exam problems
"Quantum mechanics is certainly imposing.
``...please,... stop telling God what to do.'' _________________________________________________________________________________________
OLD EXAMS
But an inner voice
tells me that
it is not yet
the real thing. The theory says a lot, but does
not really bring us closer to the secret of the
'Old One.' I, at any rate,
am convinced that He
is not playing at dice."
Einstein
Bohr
Back to Henrik Johannesson's home
page.
This page was last updated on October 13,
2003.