763613S-3005 Quantum Mechanics II 2025 / Kvanttimekaniikka II 2025 763613S-3005

Learning outcomes 

The course continues the development of the quantum mechanical frame-of-mind. By the end of the course, students will be able to proficiently apply the operator formalism to analyze quantum phenomena, including entanglement, measurements, and angular momentum. The course will also equip students with the skills to explore particle interactions using scattering theory. Additionally, students will master advanced approximation techniques, such as perturbation theory, to study weak perturbations and practical scenarios like fine-structure corrections and the Zeeman effect. 

Contents  

The course is divided into two parts. In the first part, we recap the familiar basic concepts of the wave function and postulates by introducing the state vectors and operator formalism. Modern quantum mechanical topics such as entanglement and measurements are discussed as an immediate application of operator formalism. The theory of angular momentum and spin is subsequently revisited, providing a comprehensive understanding of these concepts. Furthermore, we study interactions between particles using scattering theory, introducing concepts such as cross-section, phase shift, scattering amplitude, and Green’s function. 

The second part of the course is dedicated to an in-depth discussion of various approximative methods and their practical applications. Effects of weak perturbations are studied in terms of time-independent and time-dependent perturbation theory. As an example, we calculate fine-structure corrections to the hydrogen atom, the Zeeman effect, and the bound states of the ionic Hydrogen molecule and He-atom. The Fermi Golden Rule is derived and applied to compute radiation-induced transition rates between eigenstates. Other approximative methods, such as variational and adiabatic approximation, are also discussed. 

Prerequisites 

Quantum mechanics I, Mechanics, Atomic physics, Linear algebra, Probability calculus 

Learning activities and teaching methods

The course will be carried out through face-to-face lectures and exercise sessions. It comprises weekly lectures, exercises, reading assignments, quick quizzes, and independent work.

You can find the list with the rooms for each day (beware that it is not always the same) in Peppi.

Note that the lectures will not be recorded, but if you are unable to attend, you can find the previous year's lectures on the Moodle page with the same content.

Lectures:

 Wednesdays and Fridays at 8:15-10:00, 8.01-9.04, in total 25 lectures.

 No lectures on week 10, that is, no lectures on weeks 3.03-7.03. 

Exercises:

  • Tuesdays at 12:15-14:00, 14.01-8.04, 12 sessions.  
  • No exercises on week 10, that is, no exercises on weeks 3.03-7.03. 
  • Exercises are published on Fridays and should be returned by next Friday in Moodle.

Quick Quiz:

  • Organized at the beginning of every Wednesday lecture as group work in groups of 2-3 persons.
  • The first Quick Quiz is on Wed, 15.01. 
  • Duration 15-20 min.
  • The group discusses and answers questions on the lecture material of the week.
  • Credits towards the final assessment are earned by attending the group work.

Assessment methods and criteria

The grading is based on two midterm exams, done exercise problems, and participation in quick quizzes, or optionally one final examination.

Grading

Numerical grading scale 0 - 5 with the evaluation scale:  83 % of the whole course points yields 5/5, 75 % → 4/5, 67 % → 3/5, 58 % → 2/ 5, 50 % → 1/5. 
The total score consists of the following:
* 10 % quick quiz activity;
* 30 % exercises: 4-5 exercise problems per week, max 5 points/exercise problem;
** 1-2 points for some correct thoughts/attempts, 3 points for a serious attempt, 4 points for a correct answer with minor issues, 5 points for a completely correct answer, 6 points (extra credit) for an outstanding solution
** 70 % of the total point sum yields the maximum score on the exercises
* 30 % midterm exam 1: 4 exam problems, max 6 points each;
* 30 % midterm exam 2: 4 exam problems, max 6 points each.

Language 

The course is taught in English.

Exams

  • Midterm 1/2 Thursday 20.02 at 16:00-19:00, room L9
  • Midterm 2/2 Thursday 10.04 at 16:00-19:00, room L9 

Please get in touch with lectures via email in case you need a retake for the midterm exam.

Material

The primary material is the lecture notes and exercises that will be updated and published weekly.
* Lecture notes (spring 2023)

Recommended reading 
* Book: David J. Griffiths: Introduction to Quantum Mechanics, (Pearson Prentice Hall, 2005), the lecture notes are based on this. This book is available as an ebook:  https://oula.finna.fi/Record/oula.1471681
* Book: R. Shankar: Principles of Quantum Mechanics, (1994)
* Old lecture notes ( J. Tuorila, M. Silveri, M. Alatalo, Quantum mechanics II (English))