Quantum physics III
Summary
To introduce several advanced topics in quantum physics, including semiclassical approximation, path integral, scattering theory, and relativistic quantum mechanics
Content
1. Transition from quantum physics to classical mechanics: the coherent
states and the Ehrenfest theorem.
2. Semiclassical approximation in quantum mechanics: general form of
the semiclassical wave function and matching conditions at turning
points.
3. One-dimensional problems in semiclassical approximation:
Bohr-Sommerfeld quantisation condition and the Planck formula,
tunnelling probability through a potential barrier, lifetime of a
metastable state, splitting of the energy levels in a double-well
potential.
4. Scattering theory: cross-section, Moller operators and S-matrix,
Green's functions and the scattering amplitude, the T-matrix and the
Lippmann-Schwinger formula, perturbation theory for amplitudes and the
Born approximation, scattering amplitude via stationary scattering
states.
5. Relativistic quantum mechanics: the Dirac equation and its
non-relativistic limit - the Pauli equation.
Learning Prerequisites
Required courses
Quantum physics I, II
Learning Outcomes
By the end of the course, the student must be able to:
- Apply semiclassical considerations to solving physics problems
- Solve a number of prototypical problems of quantum physics
- Develop a connection between quantum and classical physics
- Apply scattering theory formalism to solving physics problems
Teaching methods
Ex cathedra and exercises
Assessment methods
oral exam (100%)
Resources
Bibliography
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics
L. D. Landau and E. M. Lifshitz, Quantum mechanics: non-relativistic theory
R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals
J. R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions
J. D. Bjorken, S. D. Drell, Relativistic Quantum Mechanics
A. Messiah, Quantum Mechanics
Ressources en bibliothèque
- J. D. Bjorken, S. D. Drell, Relativistic Quantum Mechanics
- (Ebook) L. D. Landau and E. M. Lifshitz, Quantum mechanics: non-relativistic theory
- C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics
- R. P. Feynman, A. R. Hibbs, Quantum Mechan
- J. R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions
- A. Messiah, Quantum Mechanics
- L. D. Landau and E. M. Lifshitz, Quantum mechanics: non-relativistic theory
Moodle Link
Prerequisite for
Quantum Physics IV
In the programs
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Quantum physics III
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 3 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Quantum physics III
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 3 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Quantum physics III
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 3 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Quantum physics III
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 3 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Quantum physics III
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 3 Hour(s) per week x 14 weeks
- Type: optional