Teaching plan for the course unit

 

 

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General information

 

Course unit name: Advanced Quantum Mechanics

Course unit code: 574634

Academic year: 2021-2022

Coordinator: Bruno Julia Diaz

Department: Department of Quantum Physics and Astrophysics

Credits: 6

Single program: S

 

 

Estimated learning time

Total number of hours 150

 

Face-to-face and/or online activities

48

 

-  Lecture

Face-to-face and online

 

32

 

-  Lecture with practical component

Face-to-face and online

 

16

Independent learning

102

 

 

Competences to be gained during study

 

Ability to develop perturbation theory approximations to known problems

Ability to develop low energy description of scattering processes

Ability to work with second quantized hamiltonians

 

 

 

 

 

Learning objectives

 

Referring to knowledge


  1. To review the basics of Quantum Mechanics and establish a common body of knowledge.

  2. To develop knowledge and understanding of the key principles and applications of Quantum Mechanics, and their relevance to current developments in physics.

  3. To become familiar with the tools of perturbation theory and other approximated resolution techniques. 

  4. To identify the solution strategies of generic Quantum Mechanics problems with a variety of tools, including those of second quantization for many-body systems; coherent states; and scattering theory. 

 

 

Teaching blocks

 

1. Foundations of quantum mechanics

*  


  1. Postulates of quantum mechanics 

  2. Dirac notation 

  3. Harmonic oscillator (ladder operators)

  4. Coherent states

  5. Angular momentum 

  6. Spin

2. Perturbation theory

*  


  1. Non-degenerate & degenerate systems

  2. Schrödinger, Heisenberg and Interaction Pictures

  3. Time-dependent perturbation theory

  4. Fermi golden rule

3. Second quantization

*  


  1. Creation & annihilation operators

  2. Fock spaces

  3. Many-body perturbation theory

4. Scattering theory

*  


  1. Lippmann-Schwinger equation

  2. Unitarity and optical theorem

  3. Partial wave expansion

  4. T-matrix and the Born approximation

  5. Scattering length and effective range

 

 

Teaching methods and general organization

 


  1. Lectures where theoretical contents of the subject are presented. 

  2. Tutorial sessions with active student and lecturer participation. 

  3. Activities related to the subject suggested by the teaching staff. 

 

 

Official assessment of learning outcomes

 


  1. A final written examination on the entire course content worth 6 points. 

  2. Members of the teaching staff may also consider students’ participation in class and in the optional tasks they suggest. 

 

 

Reading and study resources

Consulteu la disponibilitat a CERCABIB

Book

Ballentine, L. E. Quantum Mechanics: A Modern Development. World Scientific, 1998. 

Cohen-Tannoudji, C.; Diu, B.; Laloë, F.; Quantum Mechanics, Volume 2. Second Edition. Wiley & Sons, 2020.

Esposito, G.; Marmo, G.; Miele, G.; Sudarshan, G. Advanced Concepts in Quantum Mechanics, Cambridge University Press, 2015.

Merzbacher, E. Quantum Mechanics. Third Edition. Wiley & Sons, 1998.

Sakurai, J. J. Modern Quantum Mechanics. Revised Edition. Addison-Wesley, 1994