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 2021 course

Lecturer: Tuomas Lappi, office YFL240, email tuomas.v.v.lappi@jyu.fi

Teaching assistant: Jani Penttala, office YFL 353, email jani.j.penttala@student.jyu.fi

This course material is based on the material of Tero Heikkilä from spring 2020, inheriting many parts from the lecture notes of Kari J. Eskola, with some edits by Tuomas Lappi.

3. zoom meeting

link https://jyufi.zoom.us/j/62658752138

4. Contents

  • Feynman path integrals (week 1)

  • Many-body quantum mechanics (weeks 2-4)

  • Quantized electromagnetic field (week 5)

  • Relativistic quantum mechanics, Dirac equation (weeks 6-7)

5. 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 and further edited by Tuomas Lappi for the 2021 course.

  • On a large part of the course a very good material are the Advanced Quantum Mechanics lecture notes by Kimmo Tuominen, available here (link should work for students registered for the course)

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.

6. Generalities

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

  • Before Tueday's class you must read the given reading assignments for each week.
  • With the help of these you should solve some simple preliminary exercise problems: preliminary exercise questions on the TIM page for the week
  • Mark the questions that you have done on the TIM page, and be prepared to share and discuss your solutions in class on Tuesday: e.g. by scanning your solution, or writing them on a tablet with which you can call into the zoom meeting
  • On Tuesday we will have a Zoom meeting starting at 12:15. First the lecturer will discuss the material briefly. Then we split into breakout rooms to discuss the solutions in smaller groups, and then in the class together. Be prepared to share your screen 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 in the same zoom meeting (at least for now, we'll see how this works)
  • The solutions for the homework exercises 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, 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.

7. 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 the exam, 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).

8. 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).

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