FYSS7531 Quantum mechanics II A

Learning goals

After the course the student can

• Use the different pictures (Schrödinger, Heisenberg and interaction) of time dependence in quantum mechanics

• Calculate transition rates with time dependent perturbation theory (Fermi’s golden rule)

• Descibe the coupling between a classical electromagnetic field and a quantum mechanical charged particle

• Explain the basics of quantum mechanical scattering theory and use the Born approximation to calculate a scattering amplitude

• Explain the relation of quantum mechanical angular momentum to the rotation group and its representations

• Understand the concept of total angular momentum and apply the addition of quantum mechanical angular momenta to physical situations.

Spring 2021 course

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

Teaching assistant: Reena Gupta, email firstname.R.surname@jyu.fi

This is a draft set of notes to be used in the spring 2021 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.

There is also a course chat page for discussions about and around the course.

Contents

• Reminder of basic quantum mechanics, density matrix

• Scattering theory

• Quantum description of time-dependent phenomena

• Description of a classical electromagnetic field in quantum mechanics

• Adiabatic theory

• Rotations and addition of angular momenta

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 and Risto Ojajärvi.

An alternative reference is the excellent set of lecture notes by 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).

Kvanttimekaniikka II by J. Niskanen (in Finnish, available in FYS4, for sale at LIMES)

Quantum Mechanics, by Bransden and Joachain (available in FYS4). This book is very extensive, i.e. covers a lot of material, especially what is needed in this part A.

Generalities

The weekly schedule will proceed in the following way:

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

On Tuesdays we will have a Zoom meeting starting at 12:15 and lasting until the material has been discussed through, at latest by 16:00 (there will be a break in between). You can send your solutions of the preliminary exercises using the link provided on the page for the preliminary exercises. This event proceeds as follows:

• Gathering preliminary exercise points via Zoom chat (example: 1/2/0, when you give yourself 1 point for the first exercise, 2 for the second, and 0 for the third)

• You will be divided into 3 breakout rooms based on these points. There you will discuss the solution to one of the exercises and choose who will show it to the others - using their solution in TIM and Zoom annotating

• After this there is a 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: simply unmute yourself and ask.

• The lecture will be interrupted at times when we go through the preliminary exercises. This is where the students selected in the breakout rooms 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 from 12:15 to 14:00 for working on these problems together. This will also be carried out with Zoom (https://zoom.us/j/94175583692) and breakout rooms. The teaching assistant (TA) will be there to help. In the beginning of the session, you will agree on 10-minute slots when the TA will join your room. You can take an individual room or join a friend.

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.

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 ("demo"): 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.

Spring 2021 course points

Person:

Please to interact with this component.

Written exercises

Preliminary exercises

Exam

Course total