Degree | Type | Year | Semester |
---|---|---|---|
2500097 Physics | OT | 3 | 1 |
You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.
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.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
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 |
Midterm exam: 45% of the grade.
Final exam: 50% of the grade.
Exercises to be delivered: 5% of the grade.
Following rules of the university, to be able to take the make-up exam, the student must have taken first both the midterm and the final exam.
Make-up exam: 95 % of the grade.
Grading ("Avaluació Unica")
A)Final Exam (55 % of the final grade): this is a written, individual, exam at the end of the semester.
B)Oral Exam (45 % of the final grade) : this is an individual exam, at the end of the semester.
C)Make-up Exam (55% of the final grade): this is an optional exam. The grade in this exam will replace the grade in A) (avaluacio unica) in all cases.
D)Oral Make-up Exam (45 % of the final grade): this is an optional exam. The grade in this exam will replace the grade in B) (avaluacio unica) in all cases.
Both gradings will have the final exam the same day. Idem concerning the make-up exam.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Final exam | 50% | 2.5 | 0.1 | 1, 2, 6, 4, 3, 5, 7, 9, 10, 11, 12, 8, 13, 16, 14, 15, 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 |
Make-up exam | 95% | 3 | 0.12 | 1, 2, 6, 4, 3, 5, 7, 9, 10, 11, 12, 8, 13, 16, 14, 15, 18, 17 |
Midterm exam | 45% | 2.25 | 0.09 | 2, 7, 12, 8, 16, 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.
Not concieved.