Mathematical Physics II

Enrollment in class,
passed the course of Mathematical Physics I

Partial differential equations of mathematical physics: Diffusion equation, Eschroedinger equation, wave equation.

Boundary and intial conditions: Amplitude equation. Eigenfunctions of linear operators and necessary boundary conditions.

Eigenfunction expansion: Inhomogeneous amplitude equation. Homogeneous equation with inhomogeneous boundary conditions.

Separable solutions of amplitude equation: Cartesian, cylindiric and spherical coordinates. Solutions in unbounded media: propagating waves. Scattering.

Laplace equation: Solutions in different coordinate systems. Multipole expansion.

Green's functions: Solutions of inhomogeneous amplitude equations. Static and time dependent Green's functions.

Approximate methods: Perturbation expansion. Variational solutions of amplitude equations.

Integral equation of the first and second kind

I. Kuščer, A. Kodre, Matematika v fiziki in tehniki, 1994.
J. Mathews, R.L. Walker, Mathematical Methods of Physics, 1970.
G.B. Arfken, H.J. Weber, F.E. Harris: Mathematical Methods for Physicists, 2012.

Introduction and methods for solutions of basic partial differential equations of mathematical physics as the basis for further application in courses of theoretical physics.

Knowledge and understanding:
Understanding of general structure of basic equations of mathematical physics and introduction into approaches to solve such equations. Ability of mathematical formulation of physics problems.

Application:
Introduction to mathematical tools for the courses of theoretical physics.

Reflection:
Understanding of the relation between the physical phenomena and their mathematical idealization.

Transferable skills:
Solution of a concrete project with the subject of mathematical physics and the preparation of the report.

3 written tests, required 50% score
Individual project.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

prof.dr. Tomaž Prosen
152
1. T. Gorin, T. Prosen, T. H. Seligman in M. Žnidarič, Physics Reports 435, 33-
156 (2006)
2. T. Prosen, Physical Review Letters 106, 217206 (2011)
3. E. Ilievski in T. Prosen, Communications
prof.dr. Peter Prelovšek
1) P. Prelovšek and B. Uran, Generalized hot wire method for thermal
conductivity measurements, J. Phys. E 17, 674 (1984).
2) J. Jaklič and P. Prelovšek, Lanczos method for the calculation of T>0
quantitites in correlated systems, Phys. Rev. B 49, 5065 (1994).
3) P. Prelovšek and J. Bonča, Ground State and Finite Temperature Lanczos
Methods,
in Strongly Correlated Systems - Numerical Methods, eds. A. Avella and F.
Mancini (Springer Series in Solid State Sciences 176, Berlin), p. 1 - 29 (2013).
153