Path Integral

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

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 perturbative 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:

basics of quantum mechanics and Dirac's formalism

Syllabus of lectures:

1. Evolution kernel and Trotter product formula

2. configuration-space path integral

3.-4. simple solutions (free particle, harmonic oscillator, Bohm-Aharonov effect)

5. WKB approximation and its application to the anharmonic oscillator

6. variational perturbative theory and its application to the double well potential

7.-8. Green functions and the Feynman-Kac formula

9.-10. coherent state representation and Klauder's path integral

11.-12. Euclidean path integrals and applications in statistical physics

Syllabus of tutorials:

Exercise classes represent an integral part of the actual lecture. Whenever some logically consistent part of the lecture is finished, the students are asked to demonstrate their understanding in front of a blackboard. Inasmuch, the content of the exercise classes is identical with the content of the lecture.

Study Objective:

Study materials:

- R.P.Feynman and A.R.Hibbs, Quantum Mechanics and Path Integrals, (McGraw Hill, New York, 1965)

- L.S.Schulman, Techniques and Applications of Path Integration, (Wiley-Interscience, New York, 1981)

- H.Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Finacial Markets, (World Scientific Publishing, London, 2004)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: