2016 Quantum Mechanics of Many-Body Systems

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Academic unit or major
Graduate major in Physics
Nishida Yusuke 
Course component(s)
Mode of instruction
Day/Period(Room No.)
Tue3-4(H116)  Fri3-4(H116)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

Many-body quantum mechanics provides a way to describe systems consisting of many particles based on quantum mechanics.
The objective of this course is to learn the partition function represented by field functional integral (1st-4th classes), methods to treat inter-particle interactions (5th-8th classes), spontaneous symmetry breaking and its consequences (9th-12th classes), linear response theory and correlation functions (13th-15th classes).

Student learning outcomes

- Being able to explain the partition function represented by field functional integral, methods to treat inter-particle interactions, spontaneous symmetry breaking and its consequences, linear response theory and correlation functions.
- Being able to apply them to concrete problems.


field functional integral, perturbation theory, spontaneous symmetry breaking, linear response theory

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Given in a usual lecture style in English.

Course schedule/Required learning

  Course schedule Required learning
Class 1 path integral in quantum mechanics Understand contents of each lecture and be able to reproduce it on his/her own
Class 2 coherent states
Class 3 field functional integral
Class 4 partition functions of free Bose and Fermi gases
Class 5 perturbation theory and Feynman diagrams
Class 6 energy of electron gas
Class 7 random phase approximation and screening
Class 8 Fermi liquid theory and quasiparticles
Class 9 mean field approximation
Class 10 Bose-Einstein condensation and superfluidity
Class 11 superconductivity and BCS theory
Class 12 Anderson-Higgs mechanism
Class 13 measurement and linear response
Class 14 correlation funcitons
Class 15 response to electromagnetic fields


A. Altland and B. Simons "Condensed Matter Field Theory" (Cambridge University Press)

Reference books, course materials, etc.

H. Bruus and K. Flensberg "Many-Body Quantum Theory In Condensed Matter Physics" (Oxford University Press)
L. S. Brown "Quantum Field Theory" (Cambridge University Press)

Assessment criteria and methods

midterm report (30-40%) and final examination (60-70%)

Related courses

  • ZUB.Q313 : Quantum Mechanics III
  • ZUB.S310 : Thermodynamics and Statistical Mechanics II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is highly desired that students have mastered undergraduate quantum mechanics and statistical mechanics.

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