Path Integral

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

The lecture covers the following topics; Evolution kernel, Trotter product formula and configuration-space path integral, elementary properties of path integrals and simple solutions (e.g., free particle, harmonic oscillator, Bohm-Aharonov effect), semiclassical time-evolution amplitude (WKB approximation) and its application to the anharmonic oscillator, variational perturbation theory and its application to the double well potential, Green functions and the Feynman-Kac formula, phase-space path integrals, coherent state representation and Klauder's path integral, Wick rotation and Euclidean path integrals, simple applications in statistical physics.

Requirements:

Knowledge of the basic course of physics and quantum physics

Syllabus of lectures:

1.Introduction and motivation, evolution kernel, Lie-Trotter multiplicative formula, path integral in configuration space.

2.Kernel for free particle and harmonic oscilator. Semi-classical approximation, WKB method and fluctuation factor calculation.

3.Perturbative methods: variational perturbative method and an-harmonic oscillator, delta series, perturbative methods for Green functions.

4.Path integrals in phase space and Klauder path integral, Wick rotation and Euclidean path integrals, simple applications in statistical and instanton physics.

Syllabus of tutorials:

Using of methods of path integral and its application in different cases.

Study Objective:

Knowledge:

Quantization of certain systems with path integral method, construction of Green functions and quantum mechanics

Abilities:

Orientation in methods to solve quantum systems using path integral

Study materials:

Key references:

[1] L. S.Schulman, Techniques and Applications of Path Integrals, (Dover, London, 2010)

[2] H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial markets, (World Scientific, Singapore, 2014)

Recommended references:

[1] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, (Dover, New York, 2010)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: