Advanced Quantum Mechanics (WS14/15)

Lecturer

Prof. Dr. Stefan Dittmaier

Dates:

• Lecture: 4 hours, Wed 10-12, Fr 10-12, HS I,  start: 22.10.2014

• Exam: Sat, 07.02.2015, 10-13, HS I 

• Retake exam: Sat, 18.04.2015, 10-13, HS I

• Question hour: Tue, 14.04.2015, 10.15,  SR I, II, or III
  

Exercise courses:

• Contact person: Dr. Heidi Rzehak
Registration via Campus Management  (-> Belegwunsch/Stornierung) from 20.10.2014, noon, with Uni-Account.

• Dates: 2 hours, start: 29./30.10.2014
• Group 1: Wed, 14-16 (SR III)
• Group 2: Thu,  10-12 (SR I)
• Group 3: Thu,  12-14 (SR GMH)
• Group 4: Thu,  14-16 (SR I)
• Presentation of solutions: Fr, 14-16 (SR WB UG)

Content:

1. Recapitulation of basic qm. principles
   
   1. Mathematical background
      
   2. Qm. states, observables, and measurements
   3. Correspondence principle and time evolution
2. Symmetries in quantum mechanics
   
   1. Symmetry transformations and Wigner's theorem
   2. Elements of group theory
      (representations, irreducibility, Schur's lemma, finite groups, Lie groups, Lie algebras)
      
   3. Space translations
      (continuous and discrete translations, Bloch's theorem)
      
   4. Rotations
      (SO(3) and SU(2), irreducible representations, Wigner's D functions, orbital angular momentum and spin, addition of angular momenta, irreducible tensors, Wigner-Eckart theorem)
3. Approximation methods
1. WKB method
2. Time-independent perturbation theory
3. Variational method
4. Time-dependent perturbation theory
4. Scattering theory
   
   1. Potential scattering
      (Green's functions, wave packets, Lippmann-Schwinger equation, perturbation theory, partial-wave analysis, optical theorem, resonances, complex potentials)
      
   2. Basics of general scattering theory
      (T matrix, S matrix, cross sections, decay widths, general optical theorem)
      
5. Quantization of the electromagnetic field -> download
   
   1. Free electromagnetic fields
      (Classical fields, quantization in the Coulomb gauge)
      
   2. Interacting electromagnetic fields
      (Classical fields, quantization in the Coulomb gauge, 1-electron atoms in quantized radiation field)
      
6. Relativistic quantum mechanics
   

Prerequisites

Mechanics, Electrodynamics, Quantum Mechanics

Textbooks:

• Bransden/Joachain: "Physics of atoms and molecules"
  
• Cohen-Tannoudji: "Quantenmechanik, Band 1+2"
• Landau/Lifschitz: "Quantenmechanik, Lehrbuch der Theoretischen Physik, Band 3"
• Messiah: "Quantenmechanik, Band 1+2"
• Nolting:
• "Grundkurs Theoretische Physik 5/1: Quantenmechanik - Grundlagen"
• "Grundkurs Theoretische Physik 5/2: Quantenmechanik - Methoden und Anwendungen"
• Sakurai: "Modern Quantum Mechanics" and "Advanced Quantum Mechanics"
  
• Scheck: "Theoretische Physik 2: Nichtrelativistische Quantentheorie Vom Wasserstoffatom zu den Vielteilchensystemen"
• Straumann: "Quantenmechanik: Ein Grundkurs über nichtrelativistische Quantentheorie"
• Weinberg: "Lectures on Quantum Mechanics"
  
  

 Specific literature on group theory applied to QM:

• Hamermesh: "Group Theory and Its Application to Physical Problems"
• Tung: "Group Theory in Physics"
  
  

Requirements for  Course Achievement / Academic Record

• Course Achievement ("Studienleistung"):
  

  Active and regular participation in the tutorials, including solutions to 50% of the homework problems + final written exam

• Academic Record ( "Prüfungsleistung"):
  

Further details will be given in the lecture/tutorials.

Problem sheets: