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 |

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

an active knowledge of

an active knowledge of

- English

- Dutch
- English

specific prerequisites for this courseCourse notes are in Dutch. You will also need to read papers in English.

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.

- 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.

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.

The course has an international dimension.

Class contact teachingLectures Seminars/Tutorials

Personal workCase studies Individually Case studies In group

**5.3 Facilities for working students ***

Others

Personal work

Others

ExaminationWritten with oral presentation

Continuous assessmentParticipation in classroom activities

Presentation

Continuous assessment

Presentation

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

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).

Prof.dr. Jacques Tempere

N0.17, Gebouw N

UA Campus Drie Eiken

Tel: 03 265 2866