# 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
- 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