Problem Solving in Theoretical Physics

Yury M. Belousov is Researcher and Lecturer at the Moscow Institute of Physics and Technology, Dolgoprudny, Russia. Serguei N. Burmistrov is Researcher and Lecturer at the Russian Research Center "Kurchatov Institute", Moscow, Russia. Alexei I. Ternov is Researcher and Lecturer at the Moscow Institute of Physics and Technology, Dolgoprudny, Russia.

BACKGROUND AND PROBLEMS

CHAPTER 1. THEORY OF FIELDS
Introduction
1.1 Vectors and tensors in the Euclidean space
1.2 Vectors and tensors in the Minkowski space
1.3 Relativistic kinematics
1.4 The Maxwell equations
1.5 Motion of a charged particle in the external field
1.6 Static electromagnetic field
1.7 Free electromagnetic field
1.8 The retarded potentials and radiation
1.9 Electromagnetic field of relativistic particles
1.10 The scattering of electromagnetic waves

CHAPTER 2. QUANTUM MECHANICS
Introduction
2.1 Operators and states in the quantum mechanics
2.2 One-dimensional motion
2.3 Linear harmonic oscillator
2.4 Angular momentum and spin
2.5 Motion in the magnetic field
2.6 Motion in the centrally symmetric field
2.7Semiclassical approximation
2.8 Perturbation theory
2.9 Relativistic quantum mechanics
2.10 Addition of angular momenta. The identity of particles
2.11 Theory of atoms and molecules
2.12 Theory of scattering
2.13 Theory of radiation

CHAPTER 3. STATISTICAL PHYSICS
Introduction
3.1 The Gibbs distribution. The thermodynamic quantities and functions
3.2 Quantum ideal gases
3.3 Non-ideal quantum systems (liquids)
3.4 Phase transitions and the critical phenomena

SOLUTIONS TO THE PROBLEMS

CHAPTER 4. THEORY OF FIELDS
4.1 Vectors and tensors in the Euclidean space
4.2 Vectors and tensors in the Minkowski space
4.3 Relativistic kinematics
4.4 The Maxwell equations
4.5 Motion of a charged particle in the external field
4.6 Static electromagnetic field
4.7 Free electromagnetic field
4.8 The retarded potentials and radiation
4.9 Electromagnetic field of relativistic particles
4.10 The scattering of electromagnetic waves

CHAPTER 5. QUANTUM MECHANICS
5.1 Operators and states in the quantum mechanics
5.2 One-dimensional motion
5.3 Linear harmonic oscillator
5.4 Angular momentum and spin
5.5 Motion in the magnetic field
5.6 Motion in the centrally symmetric field
5.7 Semiclassical approximation
5.8 Perturbation theory
5.9 Relativistic quantum mechanics
5.10 Addition of angular momenta. The identity of particles
5.11 Theory of atoms and molecules
5.12 Theory of scattering
5.13 Theory of radiation

CHAPTER 6. STATISTICAL PHYSICS
6.1 The Gibbs distribution. The thermodynamic quantities and functions
6.2 Quantum ideal gases
6.2.1 Ideal Fermi gas
6.2.2 Ideal Bose gas
6.2.3 Ideal gas of elementary Bose excitations
6.3 Non-ideal quantum systems (liquids)
6.3.1 Normal (nonsuperfluid) Fermi liquid
6.3.2 Superconductivity. The BCS theory
6.3.3 Weakly interacting Bose gas
6.3.4 Theory of superfluidity
6.4 Phase transitions and the critical phenomena
6.4.1 The mean-field approximation
6.4.2 The Ginzburg-Landau functional
6.4.3 The fundamentals of the theory of critical phenomena

APPENDICES
1 Dirac delta function and other distributions
2 Bessel functions of half-integer order
3 Confluent hypergeometric function. The Laguerre polynomials
4 Gamma function