Problem Solving in Theoretical Physics

"e;Problem Solving in Theoretical Physics"e; helps students mastering their theoretical physics courses by posing advanced problems and providing their solutions - along with discussions of their physical significance and possibilities for generalization and transfer to other fields.

"Problem Solving in Theoretical Physics" helps students mastering their theoretical physics courses by posing advanced problems and providing their solutions - along with discussions of their physical significance and possibilities for generalization and transfer to other fields.

BACKGROUND AND PROBLEMSCHAPTER 1. THEORY OF FIELDSIntroduction1.1 Vectors and tensors in the Euclidean space1.2 Vectors and tensors in the Minkowski space1.3 Relativistic kinematics1.4 The Maxwell equations1.5 Motion of a charged particle in the external field1.6 Static electromagnetic field1.7 Free electromagnetic field1.8 The retarded potentials and radiation1.9 Electromagnetic field of relativistic particles1.10 The scattering of electromagnetic wavesCHAPTER 2. QUANTUM MECHANICSIntroduction2.1 Operators and states in the quantum mechanics2.2 One-dimensional motion2.3 Linear harmonic oscillator2.4 Angular momentum and spin2.5 Motion in the magnetic field2.6 Motion in the centrally symmetric field2.7Semiclassical approximation2.8 Perturbation theory2.9 Relativistic quantum mechanics2.10 Addition of angular momenta. The identity of particles2.11 Theory of atoms and molecules2.12 Theory of scattering2.13 Theory of radiationCHAPTER 3. STATISTICAL PHYSICSIntroduction3.1 The Gibbs distribution. The thermodynamic quantities and functions3.2 Quantum ideal gases3.3 Non-ideal quantum systems (liquids)3.4 Phase transitions and the critical phenomenaSOLUTIONS TO THE PROBLEMSCHAPTER 4. THEORY OF FIELDS4.1 Vectors and tensors in the Euclidean space4.2 Vectors and tensors in the Minkowski space4.3 Relativistic kinematics4.4 The Maxwell equations4.5 Motion of a charged particle in the external field4.6 Static electromagnetic field4.7 Free electromagnetic field4.8 The retarded potentials and radiation4.9 Electromagnetic field of relativistic particles4.10 The scattering of electromagnetic wavesCHAPTER 5. QUANTUM MECHANICS5.1 Operators and states in the quantum mechanics5.2 One-dimensional motion5.3 Linear harmonic oscillator5.4 Angular momentum and spin5.5 Motion in the magnetic field5.6 Motion in the centrally symmetric field5.7 Semiclassical approximation5.8 Perturbation theory5.9 Relativistic quantum mechanics5.10 Addition of angular momenta. The identity of particles5.11 Theory of atoms and molecules5.12 Theory of scattering5.13 Theory of radiationCHAPTER 6. STATISTICAL PHYSICS6.1 The Gibbs distribution. The thermodynamic quantities and functions6.2 Quantum ideal gases6.2.1 Ideal Fermi gas6.2.2 Ideal Bose gas6.2.3 Ideal gas of elementary Bose excitations6.3 Non-ideal quantum systems (liquids)6.3.1 Normal (nonsuperfluid) Fermi liquid6.3.2 Superconductivity. The BCS theory6.3.3 Weakly interacting Bose gas6.3.4 Theory of superfluidity6.4 Phase transitions and the critical phenomena6.4.1 The mean-field approximation6.4.2 The Ginzburg-Landau functional6.4.3 The fundamentals of the theory of critical phenomenaAPPENDICES1 Dirac delta function and other distributions2 Bessel functions of half-integer order3 Confluent hypergeometric function. The Laguerre polynomials4 Gamma function