Mathematical Physics: Problems and Solutions

The present issue of the series <Modern Problems in Mathematical Physics> represents the Proceedings of the Students Training Contest Olympiad in Mathematical and Theoretical Physics and includes the statements and the solutions of the problems offered to the participants. The contest Olympiad was held on May 21st-24th, 2010 by Scientific Research Laboratory of Mathematical Physics of Samara State University, Steklov Mathematical Institute of Russia’s Academy of Sciences, and Moscow Institute of Physics and Technology (State University) in cooperation.
The present Proceedings is intended to be used by the students of physical and mechanical-mathematical departments of the universities, who are interested in acquiring a deeper knowledge of the methods of mathematical and theoretical physics, and could be also useful for the persons involved in teaching mathematical and theoretical physics.
Contents
Introduction 4
Problems and Solutions 9
1. VIRIAL FOR ANHARMONIC OSCILLATIONS . . . . . . . . . . . . . 9
2. METHOD OF SUCCESSIVE APPROXIMATIONS . . . . . . . . . . . 10
3. EVALUATION FOR ULTRAMETRIC DIFFUSION . . . . . . . . . . . 13
4. DOUBLE EFFORT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5. RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6. THERMAL EVOLUTION EQUATIONS of the UNIVERSE . . . . . . . 20
7. ELECTRON THAT IS NOT GOING TO LEAVE . . . . . . . . . . . . 23
8. Х-SECTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9. BY THE CRADLE OF LHC . . . . . . . . . . . . . . . . . . . . . . . . 29
10. ‘WHIPPING Top-Toy’ from SAMARA . . . . . . . . . . . . . . . . . . 31
11. LAPLACIAN ∆ SPECTRUM ON A DOUGHNUT . . . . . . . . . . . 42
12. 3D DELTA FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 44
13. HEAT CONDUCTION EQUATION (HEAT SOURCE PRESENTS) . 49
14. HEAT CONDUCTION EQUATION WITH NONLINEAR ADD-ON . 53
Data on authors 57
Annex: Statements of the Problems of the Second International Olympiad 58
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Read more: http://arxiv.org

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