Introduction to the Basic Concepts of Modern Physics

These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given.

The first part is devoted to Special Relativity concerning in particular space-time relativity and relativistic kinematics.

The second part deals with Schroedinger's formulation of quantum mechanics. The presentation concerns mainly one dimensional problems, in particular tunnel effect, discrete energy levels and band spectra.

The third part concerns the application of Gibbs statistical methods to quantum systems and in particular to Bose and Fermi gasses.

Contenu

1- Introduction 2 - Special relativity 2.1 - Michelson experiment and Lorentz transformations 2.2 - Relativistic kinematics 3 - Wave mechanics 3.1 - Photoelectric effect 3.2 - Bohr's theory of quanta 3.3 - De Broglie's intepretation of Bohr's theory 3.4 - Schroedinger's equation 3.5 - Uncertainty principle 3.6 - Group and phase velocities 3.7 - Collective interpretation of the wave function 3.8 - Tunnel effect 3.9 - Discrete energy levels in potential wells 3.10 - Harmonic oscillator 3.11 - Band spectra in a periodic potential 4 - Statistical theory of matter 4.1 - Gibbs method 4.2 - Pressure and state equations 4.3 - Gran-Canonical Ensemble: Fermi and Bose gasses 5 - Appendix - Thermodynamics and Entropy