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402-0206-00L 8 Credits BSC , DR , MSC D-MATL , D-MATH , D-PHYS , D-ITET

Quantum Mechanics II

Lecturers & Examiners: Prof. Dr. Renato Renner

A repetition week is offered at the end of the semester.

VVZ CR n/a

Last Updated: 2026-06-03 00:14:17

Abstract

Many-body quantum physics rests on symmetry considerations that lead to two kinds of particles, fermions and bosons. Formal techniques include Hartree-Fock theory and second-quantization techniques, as well as quantum statistics with ensembles. Few- and many-body systems include atoms, molecules, the Fermi sea, elastic chains, radiation and its interaction with matter, and ideal quantum gases.

Objective

Basic command of few- and many-particle physics for fermions and bosons, including second quantisation, quantum statistical techniques, and path integrals. Understanding of elementary many-body systems such as atoms, molecules, the Fermi sea, electromagnetic radiation and its interaction with matter, ideal quantum gases and relativistic theories.

Content

We start with a discussion of the path-integral formalism. The description of indistinguishable particles leads us to (exchange-) symmetrised wave functions for fermions and bosons. We discuss simple few-body problems (Helium atoms, hydrogen molecule) and then proceed with a systematic description of fermionic many-body problems (Hartree-Fock approximation, screening, correlations, with applications to atoms and the Fermi sea). The second quantisation formalism allows for the compact description of the Fermi gas, of elastic strings (phonons), and the radiation field (photons). We study the interaction of radiation and matter and the associated phenomena of radiative decay, light scattering, and the Lamb shift. Quantum statistical description of ideal Bose and Fermi gases at finite temperatures concludes the program. If time permits, we will touch upon relativistic one-particle physics, the Klein-Gordon equation for spin-0 bosons and the Dirac equation describing spin-1/2 fermions.

Resources

Literature

G. Baym, Lectures on Quantum Mechanics (Benjamin, Menlo Park, California, 1969) L.I. Schiff, Quantum Mechanics (Mc-Graw-Hill, New York, 1955) A. Messiah, Quantum Mechanics I & II (North-Holland, Amsterdam, 1976) E. Merzbacher, Quantum Mechanics (John Wiley, New York, 1998) C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics I & II (John Wiley, New York, 1977) P.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (Mc Graw-Hill, New York, 1965) A.L. Fetter and J.D. Walecka, Theoretical Mechanics of Particles and Continua (Mc Graw-Hill, New York, 1980) J.J. Sakurai, Modern Quantum Mechanics (Addison Wesley, Reading, 1994) J.J. Sakurai, Advanced Quantum mechanics (Addison Wesley) F. Gross, Relativistic Quantum Mechanics and Field Theory (John Wiley, New York, 1993)

General Information

Language: English
Levels: BSC , DR , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 180 minutes
Aids: one double-sided A4 sheet with formulas

Course Components

Type	Title	Time & Place	Hours
lecture	Quantum Mechanics II	Tue 10:45-11:30 (HPH G 3) Thu 09:45-11:30 (HPH G 2)	3 h weekly
exercise	Quantum Mechanics II	Tue 11:45-13:30 (HIL D 60.1) Tue 11:45-13:30 (HIL E 10.1) Tue 11:45-13:30 (HIL E 5) Tue 13:45-15:30 (HIT J 53) Tue 13:45-15:30 (HIT K 52) Thu 07:45-09:30 (HIT J 52) Thu 07:45-09:30 (HIT K 51)	2 h weekly

Offered In

Mathematics Bachelor
- Electives
  - Selection: Mathematical Physics, Theoretical Physics (In the Bachelor's programme in Mathematics 402-0204-00L Electrodynamics is eligible as an elective course, but only if 402-0224-00L Theoretical Physics isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
Physics Bachelor
- Core Courses
  - Core Courses: Theoretical Physics
- Electives
Mathematics Master
- Application Area (Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area. Credits from other application areas cannot be recognised for further application areas.)
  - Theoretical Physics (In the Master's programme in Applied Mathematics 402-0204-00L Electrodynamics is eligible as a course unit in the application area Theoretical Physics, but only if 402-0224-00L Theoretical Physics wasn't or isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
- Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Electives: Applied Mathematics and Further Application-Oriented Fields (¬)
    - Selection: Mathematical Physics, Theoretical Physics
Doctorate Materials Science (Further information at: )
- Subject Specialisation
  - Science & Technology of the Small (MaP Doctoral School)
Quantum Engineering Master
- Electives (This is a selection of courses particularly suitable for the MSc QE. In agreement with the tutor, students may choose other courses from the ETH course catalogue.)