Degree | Type | Year | Semester |
---|---|---|---|
2500097 Physics | OT | 3 | 1 |
It is advisable to have studied the following subjects:
Calculus in one variable
Vector Calculus
Differential equations
This subject introduces some basic mathematical concepts
needed in physics in general, and in physics / Quantum mechanics
and field theories, in particular. It is intended that the student
achieve the understanding of the concepts of Hilbert space, operators, distributions
and, especially, groups. It wants to give an integrative vision
of concepts that appear in different fields in physics. At the same time,
the student will have to acquire the capacity to apply them with agility
for different types of problems.
PROGRAM
1. Hilbert spaces
1.1 Pre-Hilbert spaces.
2.2 Hilbert spaces.
2. Operators.
2.1 Linear operators.
2.2 Eigenvalues and eigenvectors.
3. Distributions
4. Introduction to group theory
4.1 Definition and motivation (symmetires)
4.2 Exemples: SO(3), SU(2), SU(N) (relation with unitary operators).
4.3 Lie algebras (generators of the continuous group)
4.4 su(N) (relation with selfadjoint operators) and relation with su(2) with so(3)
5. Representations
6. Tensorial methods
This course develops mathematical language and calculation tools that are basic
for advanced physics subjects. The personal work of the student is fundamental to attaining the pertinent knowledge and skills.
Classroom sessions will be divided into:
Lectures: The teacher will present the basic concepts and reasoning of each
Subject, with the support of examples.
Problem classes: Among a collection of problems, the teacher
will solve in detail a selection. Students will have to work on their own the rest.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Blackboard lectures: the profesor will expone basic concepts and arguments for each subject, with the support of detailed examples. | 27 | 1.08 | |
Practical lectures: among a problems collection, the professor will solve a set of them. The rest will be solved by the students. | 14 | 0.56 | |
Type: Autonomous | |||
Individual and groupal work solving problems | 28 | 1.12 | |
Selective homework | 11 | 0.44 | |
Study of teoretical foundations | 37 | 1.48 |
Partial examination of Hilbert Spaces and operators: 45% of the note.
Group partial exam: 50% of the mark.
Selective delivery of problems: 5% of the note.
By imperative of the general regulations of the university, to be able to participate in the examination of recovery must have been previously evaluated of both partial.
Resit exam of the two partials: 95% of the note. There is no minimum mark to be able to opt for the recovery.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Group theory exam | 50% | 2.5 | 0.1 | 1, 2, 6, 4, 3, 5, 7, 9, 10, 11, 12, 8, 13, 16, 14, 15, 18, 17 |
Hilbert spaces and operators exam | 45% | 2.25 | 0.09 | 2, 7, 12, 8, 16, 18, 17 |
Homework | 5% | 0.25 | 0.01 | 1, 2, 6, 4, 3, 5, 7, 9, 10, 11, 12, 8, 13, 16, 14, 15, 18, 17 |
Resit exam | 95% | 3 | 0.12 | 1, 2, 6, 4, 3, 5, 7, 9, 10, 11, 12, 8, 13, 16, 14, 15, 18, 17 |
Basic bibliografy.
P. Szekeres, A course in Modern Mathematical Physics.
Elvira Romera et al., Métodos matemáticos: Problemas de espacios de Hilbert, operadores lineales y espectros
G. Arfken, Mathematical Methods for Physics.
Advanced and complementary bibliography.
J.J. Sakurai, Modern Quantum Mechanics.
J.F. Cornwell, Group theory in Physics.
H. Georgi, Lie Algebras in particle physics.
L. Abellanas i A. Galindo, Espais de Hilbert.
S.K. Barbarian, Introducció a l'espai de Hilbert.
L. Schwartz, Métodos Matemáticos para las ciencias físicas.