Coursebooks 2017-2018

PDF
 

Quantum physics III

PHYS-425

Lecturer(s) :

Chapochnikov Mikhail

Language:

English

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. Path integral representation of quantum mechanics: Schrodinger
equation from path integral, physical interpretation of the path
integral and the principle of minimal action, Euclidean path integral
and statistical physics, "instanton" and "bounce".

 

5. 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.

 

6.  Relativistic quantum mechanics:  the Dirac equation and its
non-relativistic limit - the  Pauli equation.

Learning Prerequisites

Required courses

Quantum physics I, II

Teaching methods

Ex cathedra and exercises

Assessment methods

oral exam (100%)

Supervision

Office hours Yes

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
Moodle Link

Prerequisite for

Quantum Physics IV

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14 CM011  CM011
14-15   
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

legend

  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German