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 basic idea of quantized electromagnetic field, and properties deriving from this especially in describing transition rates
Explain the relativistic limit of quantum mechanics, and use the Dirac equation to describe spin-1/2 particles in the relativistic limit

2. Spring 2022 course

Lecturer: Pauli Virtanen, office YNC 223.2, email pauli.t.virtanen@jyu.fi

Teaching assistant: Andrii Sokolov, YNC 221, email andriy145@gmail.com

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 edits by Tuomas Lappi for 2021 course, and PV for 2022.

3. Contents

Feynman path integrals (week 1)
Many-body quantum mechanics (weeks 2, 3, 4)
Quantized electromagnetic field (week 5)
Relativistic quantum mechanics (weeks 6, 7)

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 and further edited by Tuomas Lappi and P.V. for the 2021 and 2022 courses.

These lecture notes have several "+" sections that you can open. They contain extra material: reminders from previous courses, quizzes, and possibly interesting digressions beyond the scope of this course.

Different parts of 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.
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)

5. Practicalities

First lecture on March 15th, last exercise on May 5th.

Zoom link for lectures: https://jyufi.zoom.us/j/61696057127

Zoom link for exercises: https://jyufi.zoom.us/j/69019899301

Lectures and exercises are done as follows. Each week:

Before Tuesday's class: Read the reading assignments for that week, and solve the pre-exercise problems, based on that material. Be prepared to share and discuss them in the class. The pre-exercises can be found on at the beginning of that week's lecture notes on TIM. Mark there also which pre-exercises you have done on scale 0-2 for each question, before the class.

Tuesday's class (12:15-16:00, with break): face-to-face meeting in FYS5; Zoom available. We'll proceed as follows: You'll be divided to 3 groups based on these points, to discuss the solutions of the exercises and choose who will present it to the others. After that, we discuss the material of that week, interleaved with presentations of the solutions to the exercise problems.

After Tuesday's class: Work on homework exercise problems. These can be found on TIM each week.

Thursday's class (12:15-14:00, FYS5); Available online: This is a tutorial session where you can work on the homework problems together, with help from TA.

By Sunday 12:00, return your solutions to the homework exercise problems. They should be uploaded in electronic form (scanned PDF) to TIM. The upload forms are on the same page as the exercise sheet.

After the deadline, model solutions to the exercise problems appear on TIM on the exercise page. Self-grade your own solutions, on scale 0-3 points per problem. You can use a different pen to correct and complement your solutions. By Monday 9pm, upload the self-graded solutions again in TIM. The TA will check your grading, record the exercise points, and give extra points if you have successfully corrected your solutions. Just copying the model solution does not give any extra credit.

Exams are on May 10 / 11 / 17; we will agree a separate time between 10:00-16:00 for each participant.

6. Evaluation

Parts

Written exercises 40%
Pre-exercises 20%
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.

The TA will check your grading, record the exercise points, and give extra points if you have successfully corrected your solutions. Just copying the model solution does not give any extra credit.
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.