Theoretical Physics V (Advanced Concepts of Quantum Physics)

G. Morigi mit R. Menu, G. Harmon, E. King, R. Krill

Vorlesung

  • Montag 12:15 - 14:00 Uhr, Gebäude E2 6 - Seminarraum E04
  • Dienstag 12:15 - 14:00 Uhr, Gebäude E2 6 - Seminarraum E04

Vorlesungsbeginn: Montag, 15.04.2023, 12:00 Uhr

Übungen

ACHTUNG: Bitte schreiben Sie eine E-Mail an emma.king@physik.uni-saarland.de, um sich bei den Übungsgruppen anzumelden.

Exercise groups

Tutorium:

Klausuren

Erste Klausur : Mi., 31.07.2024 von 09:00 bis 12:00 Uhr, Gebäude C6 4, der gr. HS der Physik
Zweite Klausur : Do., 19.09.2024 von 09:00 bis 12:00 Uhr, Gebäude C6 4, der gr. HS der Physik

Übungsblätter

Prüfungsleistungen

  • Prüfungsvorleistung: Mindestens 50% der Votierpunkte und Vorrechnen einiger Aufgaben. Das Ankreuzen einer Aufgabe entspricht einer verbindlichen Bereitschaft, den entsprechenden Lösungsweg an der Tafel zu präsentieren. Bei Verweigerung werden die jeweiligen Punkte aberkannt. Wurde die entsprechende Prüfungszulassung bereits früher erworben, entfallen diese Vorleistungen.
  • Bestehen einer der beiden Klausuren (die bessere wird gewertet).

Inhalt der Vorlesung

Note: The program of TP5E includes all material till the end of Section 4.

0. Resume

  • 0.1 One-particle theories and the continuity equation
    • The continuity equation of non-relativistic quantum mechanics
    • Klein-Gordon equation and a naive attempt to derive a continuity equation
  • 0.2 The covariant notation of special relativity


1. The Dirac Equation

  • 1.1 Derivation of Dirac Equation and basic properties
  • 1.2 Transformations between inertial reference frames
  • 1.3 The Dirac equation in covariant notation
  • 1.4 Conservation laws for free electrons
  • 1.5 Elementary solutions of the Dirac equation
  • 1.6 Hole theory and the positron
  • 1.7 Charge conjugation
  • 1.8 Dirac equation with fields
  • 1.9 The Hydrogen atom

 

2. Scattering theory (1st part)

  • 2.1 Dyson series and non-relativistic perturbation theory
    • 2.1.1 First order perturbation theory and the Fermi golen rule
    • 2.1.2 Second order perturbation theory
    • 2.1.3 On the validity of the perturbative expansion to second order
  • 2.2 The scattering matrix
  • 2.3 Example: non-relativistic bound electron interacting with fields

 

3. The quantum electromagnetic field

  • 3.1 Lagrangian density of the electromagnetic field
    • 3.1.1 Discrete mechanical systems
    • 3.1.2 Continuum systems: the Lagrangian density and Euler-Lagrange equations
    • 3.1.3 Classical scalar fields
    • 3.1.4 The Lagrangian density of the electromagnetic field
  • 3.2 Quantization of the electromagnetic field Hamiltonian
    • 3.2.1 The radiation field as a collection of harmonic oscillators
    • 3.2.2 Quantization of the radiation oscillators
  • 3.3 Vacuum fluctuations
    • 3.3.1 Frequency cutoff
    • 3.3.2 Casimir effect
  • 3.4 The classical limit


4. Photon-Matter interactions

  • 4.1 The minimal coupling Hamiltonian in the non-relativistic limit
  • 4.2 Matrix elements of the perturbation
    • 4.2.1 Free electron interacting with the emf: fundamental processes
    • 4.2.2 Bound electron interacting with the emf
      • 4.2.2.1 Electric-dipole approximation
      • 4.2.2.2 Matrix elements in electric-dipole approximation
      • 4.2.2.3 Fundamental processes
  • 4.3 Spontaneous decay of the excited state of an atom
  • 4.4 The Lamb Shift
  • 4.5 Scattering processes


5. Second Quantization

  • 5.1 Classical fields
    • 5.1.1 Scalar fields
    • 5.1.2 From classical to quantum scalar fields
  • 5.2 Second quantization (non-relativistic fields)
    • 5.2.1 change of basis
  • 5.3 Relativistic scalar fields
    • 5.3.1 Real scalar field
    • 5.3.2 Complex scalar field

 

6. Noether's theorem

  • 6.1 The principle of stationary action
  • 6.2 Noether's theorem
    • 6.2.1 Translational invariance and the canonical energy-momentum tensoe
    • 6.2.2 Gauge invariance

 

7. Dirac Fields

  • 7.1 Lagrangian density
  • 7.2 Dirac fields
  • 7.3 Positron operator

Literatur

  • J. J. Sakurai “Advanced Quantum Mechanics” (Pearson Education, 2006)
  • F. J. Dyson "Advanced Quantum Mechanics" (WSPC, 2011)
  • K. Huang, "Quantum Field Theory", Wiley and Son Ed.