Path Integral
Code  Completion  Credits  Range  Language 

02DRI  Z,ZK  3  2+1  Czech 
 Lecturer:
 Petr Jizba (guarantor)
 Tutor:
 Petr Jizba (guarantor)
 Supervisor:
 Department of Physics
 Synopsis:

The lecture covers the following topics; Evolution kernel, Trotter product formula and configurationspace path integral, elementary properties of path integrals and simple solutions (e.g., free particle, harmonic oscillator, BohmAharonov effect), semiclassical timeevolution 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 FeynmanKac formula, phasespace 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, LieTrotter multiplicative formula, path integral in configuration space.
2.Kernel for free particle and harmonic oscilator. Semiclassical approximation, WKB method and fluctuation factor calculation.
3.Perturbative methods: variational perturbative method and anharmonic 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 timetable has been prepared for this course
 The course is a part of the following study plans:

 Experimentální jaderná a částicová fyzika (elective course)