- Term: Fall 2016.
- Course codes: AMATH 473/673, PHYS454
- Instructor: Achim Kempf
- Prerequisite: AMATH 373 or PHYS 434, or consent of instructor.
- Lecture times: Mondays and Wednesdays, 11:30am - 12:50pm.
But there are 2 cancelations and 2 make-up lectures:
- No class on Mon. Oct. 10 (Thanksgiving)
- No class on Wed. Oct 12 (Fall break)
- Extra class on Fri. Oct.14 at 11:30-12:50pm in MC1056.
- Extra class on Mon. Dec 5 at 11:30am-12:50pm in MC1056
- Venue: MC 1056
- Grades (undergraduate): Homework 25%, Midterm 25%, Final 50%.
- Grades (graduate): Essay (see below) 1/3, remaining 2/3 as for undergraduate students.
- Graduate students (those who enrolled in AMATH673):
Homework, midterm and final will be the same as for undergraduate students. Plus, graduate students hand in a 10 page essay on the topic of the "Berry phase" by 11:59pm on December 1st. For advice on writing an essay, see the bottom of this page. - Midterm exam: Monday, November 14, in class: 11:30-12:50pm in MC1056.
- Final exam: Friday, 9 December, 12:30-3:00pm in MC4045.
- Special Office hours in the week of the final exam:
- TA (Aida Ahmadzadegan): Wednesday 9-11am (in PHYS207)
- Instructor (Achim Kempf): Wednesday 4-6pm (in MC6322/MC6334)
- TA (Paul Tiede): Thursday 12-2pm (in MC6334)
- Anonymous feedback form (very helpful - please fill in any time, I keep reading it): here
Lecture notes
Lecture notes by Jason Pye: 1, 2, Images
Lecture notes: Chapters 1,2,3,4,5,6,7,8,9,10,11
Homework listed in Ch.2: due in class on Mon. Oct. 3rd
Homework listed in Ch.3: due in class on Fri. Oct. 14th, at 11:30am
Homework listed in Chs.4,5: due in class on Wed. Oct. 26 at 11:30am
Homework listed in Ch.6: due in class on Mon. Oct. 31 at 11:30am
Homework listed in Ch.7 up to p.106 (but excluding exercise 7.10 because we didn't quite cover this yet): due in class on Mon. Nov. 7 at 11:30am
Homework listed in Ch.7 starting from exercise 7.10: due in class on Wed. Nov 16, at 11:30am.
Homework listed in Ch.8: due in class on Wed. Nov. 23 at 11:30am.
Homework listed in Chs.9,10: due in class on Wed. Nov. 30 at 11:30am.
Content
The fact that everything in nature behaves quantum mechanically has been used to humanity’s advantage in numerous applications, from semi-conductors to superconductors and from solar panels to lasers. Upcoming practical applications of quantum phenomena are, for example, quantum computers, quantum communication devices and quantum measurement instruments.
On the level of pure discovery, much progress is being made, for example, in the field of cosmology: Quantum theory predicts that quantum fluctuations shortly after the big bang were what caused the statistical distribution of galaxies in the universe. Recent observations with ground and satellite-based telescopes closely match the predictions!
The aim of AMATH 473 / PHYS 454 is to give a solid understanding of the mathematical structure which underlies quantum theory. The course should provide a basis from which interested students can proceed, for example, to studies of quantum technologies, or to studies of the quantum theory of fields, which can then lead, for example, to particle physics and to quantum gravity and cosmology.
In AMATH 473 / PHYS 454, we will, therefore, study the internal workings of quantum mechanics, in its abstract formulations by Heisenberg, Schroedinger, Dirac and Feynman, as well as practical perturbative tools for applying quantum mechanics to real-live systems. We will investigate the relation between Bose-Einstein and Fermi statistics, symmetries and conservation laws, and we will cover Bell's paradox, open quantum systems, decoherence and thermal states.
Textbooks: Recommended are the modern texts by Griffiths, Cohen-Tannoudji, Shankar and Sakurai, as well as the classics by Feynman Hibbs (path integral, ingenious) and Messiah (operator formalism, very comprehensive: >1000 pages). The two classics are now very cheap (from Dover).
General advice on what is expected in the essay (graduate students only)
- Format: title and abstract page/motivation/main parts/summary (or conclusions)/bibliography.
- Bibliography: List all of your sources explicitly. Of course you can use Wikipedia but you should not cite it - because it can change from day to day and because as it is not (yet) reliable enough to meet scientific standards. Instead, cite books and papers that you may have found via Wikipedia. Also, it is good style to list items in the bibliography in that sequence in which they are first referred to in the text.
- At most about 10 pages.
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An essay should be a review of existing literature on a given topic. The sources can be textbooks, lecture notes or review articles or original articles or some of each. All and everything that is used needs to be cited. Most articles are now available online and for example "Google Scholar" can get you there quickly. Try for example searching for a few key words along with the words "review" or "introduction". Most electronic journals require a subscription, which the university library usually has. For the license to be recognized you may need to browse either from a university computer (the domain is what counts) or you log into the library website from home and go to an electronic journal through the library's electronic journal search engine.
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In the essay, your task is to show that you have understood and critically reflected upon the material by making it your own. You make it your own by coming up with an original way for presenting the material that you are bringing together. Try to give it your own angle or spin. Wherever possible, try to put things into a larger context. Sometimes (hopefully very rarely) it may be necessary to stick quite closely to a source, e.g., when a calculation is to be presented and the source does it in a way that is just hard to improve upon. In this case, you can make it your own for example by filling in a few steps in the calculation that the author omitted. In this case, it is important that you point out at that place that you do so. Filling in steps obviously proves that you understood that calculation.
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A good essay describes. An excellent essay explains.
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No original research is expected. But, you are encouraged to make educated speculations about what interesting things could be done in this area. You have been a regurgitating undergraduate for a long time. This is an opportunity to show that you still have some creativity left in you! Don't worry, you are not expected to solve the problem of quantum gravity here. Just show that you are thinking for yourself.