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Path Integrals in Quantum Mechanics

Course Code :	2002WETPQM
Study domain:	Physics
Bi-anuall course:	Taught in academic years starting in an odd year
Academic year:	2019-2020
Semester:	1st semester
Contact hours:	30
Credits:	6
Study load (hours):	168
Contract restrictions:	No contract restriction
Language of instruction:	English
Exam period:	exam in the 1st semester
Lecturer(s)	Jacques Tempere

1. Prerequisites *

At the start of this course the student should have acquired the following competences:
an active knowledge of

English

a passive knowledge of

Dutch
English

Course notes are in Dutch. You will also need to read papers in English.

specific prerequisites for this course

You need to have followed basic quantum mechanics course, in particular quantum dynamics, Dirac's bra-ket formalism, Schrodinger wave mechanics and Heisenberg matrix mechanics.

2. Learning outcomes *

You are familiar with the concepts of path integral theory, and you can explain these concepts clearly, and contrast them with the Schrodinger and Heisenberg versions of quantum mechanics.
You can quantize a classical theory using path integrals.
You can use path integrals to calculate quantum statistical expectation values.
You can find exact solutions for path integrals of quadratic Lagrangians, and calculate analytic expressions for the propagator.
You can use the WKB method and Jensen-Feynman variation to estimate path integrals for more complicated Lagrangians.
You can perform a thorough study of a specific application of path integration. Examples of this in-depth study are: superfluidity in liquid helium, the Aharanov-Bohm effect and particles on a ring, the Duru-Kleinert description of the hydrogen atom, and relativistic particles.

3. Course contents *

We start by explaining and introducing the concept of path integration, deriving it from the two-slit experiment, and contrast this approach to quantum mechanics with other approaches (namely the Schrodinger and Heisenberg approaches). Also the link with quantum statistical mechanics is explained.
In the second part, you learn techniques to calculate path integrals. We take a close look at: the exact solutions for quadratic path integrals, fourier methods, the WKB method, and the method of images. We solve a number of representative cases, that serve as references for later use.
In the third part, you pick a specific specialized topic (eg. superfluidity in liquid helium, the Aharanov-Bohm effect and particles on a ring, the Duru-Kleinert description of the hydrogen atom, relativistic particles) and explore how path integrals are used in these more complicated, real-life examples. You report on your study through a didactic presentation for your other students, so they can also understand this topic.

4 International dimension*

The course has an international dimension.

The lecturer teaches in a language other than Dutch

The lecturer uses course materials in a foreign language

5. Teaching method and planned learning activities

Class contact teaching

Lectures

Seminars/Tutorials

Personal work

Case studies Individually

Case studies In group

5.3 Facilities for working students *

Others

6. Assessment method and criteria

Examination

Written with oral presentation

Continuous assessment

Participation in classroom activities

Presentation

7. Study material *

7.1 Required reading

Your own notes during class, and papers provided for the advanced topic.

7.2 Optional reading

The following study material can be studied voluntarily :

A course syllabus in Dutch is available. Additionally, you can consult:
R. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals: Emended Edition (2010).
L. Schulman, Techniques and Applications of Path Integration (Wiley Interscience, 1996).
H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets (World Scientific Publishing, 2009).

8. Contact information *

Prof.dr. Jacques Tempere
N0.17, Gebouw N
UA Campus Drie Eiken
Tel: 03 265 2866