Teacher(s)
Language
English
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Prerequisites
Having followed LPHYS1202 is an asset.
Main themes
This teaching unit aims at presenting and deepening the mathematical structures supporting the construction of modern physics theories. These structures will be presented according to the logical flow in which they can be constructed. Various practical examples taken from actual physics will be used as an illustration of their importance.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 |
a. Contribution of the teaching unit to the learning outcomes of the programme (PHYS2M and PHYS2M1) 1.2, 2.1, 2.5, 3.1, 3.2, 3.3, 3.4 b. Specific learning outcomes of the teaching unit At the end of this teaching unit, the student will be able to : 1. express the axioms supporting the mathematical structures seen in the lectures ; 2. express and demonstrate the main theorems used in physics ; 3. generalize and apply the techniques seen in the lectures to new problem in physics. |
Content
This course offers an introduction to the mathematical structures underlying quantum theory. It covers selected chapters of functional analysis, such as Banach and Hilbert spaces, operators and spectral theory, elements of measure and integration theory, and distributions and Green’s functions.
Teaching methods
The learning activity consists of lectures. They introduce the fundamental mathematical concepts and highlight their role in the formulation of quantum mechanics and quantum field theory. Exercises will be provided to foster a progressive deepening of the concepts introduced.
Evaluation methods
Evaluation is based on a written examination covering the theoretical notions and their applications to problems in mathematical physics. It assesses students' understanding of the concepts studied in the course, their ability to employ mathematical tools to analyse problems arising from quantum mechanics and quantum field theory, as well as their proficiency in calculation techniques and the coherent presentation of solutions.
Online resources
Bibliography
- G. Teschl, Mathematical Methods in Quantum Mechanics, AMS, 2014.
- R.G. Bartle, The Elements of Integration and Lebesgue Measure, Wiley, 1995.
- L. Schwartz, Mathematics for the Physical Sciences, Dover, 2008.
Faculty or entity
