Mathematical Physics II

• knowledge of mathematical models of physical problems from classical and quantum physics;
• mastering of solving the mathematical models of physical problems using differential and integral equations, and the calculus of variations.

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1. Partial differential equations (PDEs). Time independent problems. Time dependent problems. Linear second-order PDEs. Laplace's equation. Harmonic functions. The wave equation. Poisson's equation. Schrödinger's equation. Green's functions. Separation of variables; Boundary Value Problems. Fourier transforms.

2. Calculus of variations. Euler-Lagrange equation. Variational problems with constraints. Hamilton's principle.

3. Linear integral equations. Solution methods. Separable kernel. Neumann series. Transformation to differential equation. The Schmidt-Hilbert solution. Application to boundary problems. Physical examples.

Students will learn:

• how to correctly formulate mathematical models to describe the steady state and the time- dependent evolution of physical systems;
• how to apply the basic methods of mathematical physics in addressing the statics and dynamics of physical systems on examples from classical and quantum physics.

Basic:

• E. Kreyszig, Advanced engineering mathematics, Wiley (2006). Catalogue E-version
• L. Elsgolts, Differential equations and the calculus of variations, U.Press of Pacific (2004). Catalogue E-version
• T. Chow, Mathematical methods for physicists: a concise introduction, Cambridge (2000). Katalog E-version

Additional:

• Arfken, H. Weber, F. Harris, Mathematical methods for physicists, Elsevier (2012). Catalogue E-version
• I. Kuščer, A. Kodre, Matematika v fiziki in tehniki, DMFA, Ljubljana (2006). Catalogue

• completed homework
• written exam

Dr. Sergey Vorobyev je docent za področje fizike na Univerzi v Novi Gorici.
Dr. Sergey Vorobyev is assistant professor of physics at the University of Nova Gorica.
Njegova raziskovalna dejavnost je povezana z eksperimentalno fiziko kozmičnih žarkov in astronomijo gama žarkov zelo visokih energij.
Izbrane objave / selected publications:
Pierre Auger Collaboration, AAB, A., VOROBIOV, Serguei, et al., Observation of a large-scale anisotropy in the arrival directions of cosmic rays above 8×1018 eV. Science, ISSN 0036- 8075, sep. 2017, vol. 357, iss. 6357, str. 1266-1270, ilustr., doi: 10.1126/science.aan4338.
[COBISS.SI-ID 4921595].
SCHWANKE, U., VOROBIOV, Serguei, et al., A versatile digital camera trigger for telescopes in the Cherenkov Telescope Array. Nuclear instruments and methods in physics research. Section A, ISSN 0168-9002, 2015, vol. 782, str. 92-103, doi: 10.1016/j.nima.2015.01.096.
[COBISS.SI-ID 3758075].
CTA Consortium, ACTIS, M., VOROBIOV, Serguei, et al. Design concepts for the Cherenkov Telescope Array CTA : an advanced facility for ground-based high-energy gamma-ray astronomy. Experimental astronomy, Astrophysics and space science, ISSN 0922-6435, 2013, vol. 32, no. 3, str. 193-316, doi: 10.1007/s10686-011-9247-0. [COBISS.SI-ID
3234555].
VOROBIOV, Serguei, et al., NECTAr : new electronics for the Cherenkov Telescope Array. Nuclear instruments and methods in physics research A, ISSN 0168-9002, vol. 639, no. 1, 2011, str. 62, doi: 10.1016/j.nima.2010.08.112. [COBISS.SI-ID 3233787].
H.E.S.S. Collaboration, ABRAMOWSKI, A., VOROBIOV, Serguei, et al. Search for a dark matter annihilation signal from the galactic center halo with H.E.S.S. Physical review letters, ISSN 0031-9007. [Print ed.], apr. 2011, vol. 106, 161301-1-161301-5, doi:10.1103/
PhysRevLett.106.161301. [COBISS.SI-ID 3232251].
VOROBIOV, Serguei, HUSSAIN, Mustafa, VEBERIČ, Darko. Studies of UHECR propagation in the galactic magnetic field. V: CAPDEVIELLE, Jean-Noël (ur.), ENGEL, Ralph (ur.), PATTISON, Bryan (ur.). ISVHECRI 2008 : proceedings of the XV International Symposium on Very High Energy Cosmic Ray Interactions, Paris, France, 1-6 September 2008, (Nuclear physics B, Proceedings supplement, ISSN 0920-5632, Vol. 196).
Amsterdam: Elsevier, 2009, vol. 196, str. 203-206. [COBISS.SI-ID 1305083].
DJANNATI-ATAI, A., VOROBIOV, Serguei, et al. Detection of the BL Lac Object 1ES 1426+428 in the very high energy gamma-ray band by the CAT telescope from 1998- 2000. Astronomy & astrophysics, ISSN 0004-6361, 2002, let. 391, št. 3, str. L25-L28.
[COBISS.SI-ID 564731].