FYSS7532 Quantum mechanics II B

1. Learning goals:

At the end of the course, the students will be able to

  • Explain the idea of Feynman path integrals and use them in some elementary cases

  • Identify and explain the basic starting point of many-particle quantum mechanics

  • Apply the formalism of second quantization for the description of many-particle phenomena both for bosons and fermions

  • Explain the basic principle of the Fermi gas and some of its properties

  • Apply mean field theory in describing interacting many-particle systems

  • Explain the relativistic limit of quantum mechanics, and use the Dirac equation to describe spin-1/2 particles in the relativistic limit

  • Explain the basic idea of quantized electromagnetic field, and properties deriving from this especially in describing transition rates

2. Spring 2020 course

Lecturer: Tero Heikkilä, office YN214, email firstname.T.surname@jyu.fi

Teaching assistants: Yao Lu, office YN251, email firstname.Y.surname@jyu.fi, and Camillo Tassi, office YN221, email surnamecx@jyu.fi.

This is a draft set of notes to be used in the spring 2020 course. It is the first time these notes are used in TIM, so there will be some errors. Please make a note of those errors with the commenting function so we can get rid of as many of them as possible.

The lectures are carried out by remote teaching and the videos of the Zoom session are stored on this page.

4. Literature

The primary literature consists of this set of lecture notes. They are mostly based on the set of hand-written notes by Kari J. Eskola and which have been adapted to TIM and appended by Tero T. Heikkilä, Risto Ojajärvi and Kalle Kansanen.

An alternative reference is the excellent set of lecture notes on advanced quantum mechanics by Kimmo Tuominen (University of Helsinki).

Some of the material is of course also available in many books, such as

Yu.V. Nazarov & J. Danon: "Advanced quantum mechanics" (ISBN 978-0521761505) or

"Modern Quantum Mechanics" by J.J. Sakurai (older edition, you might try looking for this online), newer edition by J.J. Sakurai and J. Napolitano (available in FYS4).

5. Generalities

Updated to allow for complete remote teaching

The division of these between lectures and exercises will not follow the labeling in Korppi. The weekly schedule will proceed in the following way:

Before Tueday's class you must read the given reading assignments for each week (see this page). With the help of these you should solve some simple preliminary exercise problems and be prepared to discuss your solutions on Tuesday.

On Tuesday we will have a Zoom meeting starting at 12:15. You can send your solutions of the preliminary exercises using the link provided on that page. We will start by gathering a list of points as usual, but via the Zoom messaging. Then there is a video lecture, where the lecturer will share his screen and show the main points via slides or via the Tim page. Here you can also ask questions. The method is such that you unmute your microphone when you have a question. The video lecture will be interrupted at times when we go through the preliminary exercises. This is where the students share their screens and explain.

After the Tuesday class you should start working on the main homework exercise problems.

The class on Thursday will be a tutorial session for working on these problems together. This will also be carried out with videoconferencing. The plan is to have individual timed tutoring sessions with the teaching assistants.

The solutions must be returned in electronic form using the form in the exercise page, as a (scanned handwritten) pdf document, by Friday 9 pm (note that this time may still change). After the solution return deadline you will get access to suggested solutions (hand written by the lecturer, please ask if the writing is unintelligible). With the help of these solutions must now grade your own solutions on a scale of 0 to 3 points per problem. At this stage you can (using a different color pen) correct and complement your solutions. Your self-graded problem answers must then be returned again in TIM, by Monday at 14. The TA will check that you have been honest in your grading, record the exercise points, and give extra points if you have successfully corrected or complemented your solutions. Just copying the model solution does not give any extra credit.

NB: every week there are two sets of exercise problems:

  • The preliminary exercises which you should do while reading the assignment, these will be discussed in groups in class on Tuesday.
  • The written exercises, for which you hand in your solutions in writing by Friday night and again your self-graded solutions by Monday.

6. Evaluation

Parts

  • Written exercises 40 %

  • Preliminary exercises 20 %

  • Oral exam 40 %

These parts will be graded separately. The final grade is a weighted average of the normalized total points from different parts, with weights as indicated above.

Evaluation criteria:

  • Self-evaluation of written exercises: 0-3 p/exercise. One point requires a significant effort to solve the problem, and the checking and correcting it afterwards.

  • Preliminary exercises: 0-2 p/exercise as a self-evaluation. 2 p, if the student is ready to explain the solution, 1 p, if enough prepared to contribute to the group discussion on the problem.

  • Oral exam: 4-5 exercises selected randomly from a list of exercises given before, 2 evaluators with separate grading (3 p: good solution without essential help, 2 p: good solution after help, 1 p: partial answer even after help, 0 p: no proper solution). The end result is scaled so that the maximum is 40 points.

Course evaluation is maintained on this page.

7. Using these notes in other courses?

If you are interested in using and modifying these notes to be used in your course, please contact Tero Heikkilä (firstname.t.surname@jyu.fi).

These are the current permissions for this document; please modify if needed. You can always modify these permissions from the manage page.