| TFYA18 |
Mathematical Methods of Physics, 6 ECTS credits.
/Fysikens matematiska metoder/
For:
MFYS
Y
|
| |
Prel. scheduled
hours: 48
Rec. self-study hours: 112
|
| |
Area of Education: Science
Main field of studies: Physics, Applied Physics
|
| |
Advancement level
(G1, G2, A): A
|
|
Aim:
The course is aimed at making the students familiar with the basic equations of the mathematical physics and the methods of their solutions. The emphasis will be done on the special functions involved in the solution of these equations. It will be given much attention to the visualization of the solutions for a number of typical physical problems of current interest.
To achieve this goal students have to
- model physical systems in mechanics, hydrodynamics, electrodynamics and quantum mechanics by the wave and heat transfer equations, Poisson, Laplace and Schrödinger equations;
- explore the methods of the solutions of these equations in rectangular, cylindrical and spherical coordinates
with corresponding boundary and initial conditions;
- know the properties and how to use in practice the Bessel functions, Legendre polynomials,
associative Legendre polymomials, Lagerre and Hermitian polynomials;
- analyze and visualize the solutions in terms of special functions;
- get knowledge of the methods of the random processes theory from the description of correlations in mesoscopic systems.
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Analysis, Linear algebra, Vector analysis, Complex analysis, Fourier analysis.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
|
|
Organisation:
Seminars including theory and problem solving following a special plan presented at the beginning of the course. Labs including numerical solutions of partial differential equations.
|
|
Course contents:
Basic equations of mathematical physics and methods of their solutions: separation of variables, orthogonal set expansion, Fourier- and Laplace integral transforms, Green's functions. Sturm-Liouville problem. Bessel functions. Fourier-Bessel series. Boundary value problems in potential theory. Legendre and associative Legendre polynomials. Application of Legendre polynomials in potential theory. Spherical harmonics. Temperature and potential problems in spherical symmetry. Schrödinger equation in cylindrical and spherical symmetry. Theory of Brownian motion. Langevin equation. Fokker-Planck equation. Long-lived correlations in mesoscopic systems. Visualization of the solutions of wave and heat transform equations, vibration of a circular membrane, potential problems in cylindrical and spherical symmetry, hydrogen atom and free particle in central force problem, temperature distribution in a cylindrical bar and a sphere.
|
|
Course literature:
I.I. Yakymenko. Lecture Notes in Mathematical Methods in Physics.
I.I. Yakymenko. Set of Problems in Mathematical Methods in Physics.
|
|
Examination: |
|
A written examination containing theory problems and practical soulution of problems (U,3,4,5)
|
6 ECTS
|
| |
|
|
Course language is English.
Department offering the course: IFM.
Director of Studies: Magnus Johansson
Examiner: Iryna Yakymenko
Link to the course homepage at the department
Course Syllabus in Swedish
|