Advanced Quantum Mechanics (WS18/19)

Lecturer

Prof. Dr. Stefan Dittmaier

Dates

• Lecture: 4 hours, Wed 10-12, Fri 10-12, HS I, start: 17.10.2018
• Exercise classes: 2 hours, start: 22./23./24.10.2018. The online registration for the exercise classes is closed.
  
• Presentation of the solutions (not mandatory for course achievement): Fri 14-16, HS II.
  

• Exam: Sat, 02.02.2019, 13:00-16:00, HS I.
  Presentation of the solutions: Fr, 08.02.2019, 14:15, HS II.
  Post-exam review: Fr 08.02.2019 in HH0815, subsequent to the presentation of the solutions.

• Resit exam: Sat, 13.04.2019, 10-13, HS I.
  Post-exam review: Do 18.04.2019, 14:15, in HH0815.
  
• Allowed aids in the exams:
  
  • A book of mathematical formulas,
  • a hand-written A4 sheet, both sides.

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
   
   1. Free electromagnetic fields
   2. (Classical fields, quantization in the Coulomb gauge)
      
   3. 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

Literature

• 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"
• Ramond: "Group Theory: A Physicist's Survey"
  

Requirements for Course Achievement / Academic Record

• Active and regular participation in the tutorials, including solutions to 60% of the homework problems.

• Final written exam.

Problem sheets