Introduction to the basic concepts of modern physics : special relatively, quantum and statistical 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 three dimensional Schroedinger equation is discussed in the case of a cubic box and in that of central potentials; in particular we give some details on the harmonic oscillator, the spherical box and the Coulomb potential. The third part concerns the application of Gibbs statistical methods to quantum systems and in particular to Bose and Fermi gasses.

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Becchi and D'Elia (Istituto Nazionale di Fisica Nucleare, Genoa) present in one book of lecture notes the topics that constituted the break with classical physics at the turn of the 20th century. Special relativity and statistical and quantum physics are presented at an introductory level but with the mathematical rigor requiring a prior course in classical mechanics. As such, this book is geared toward undergraduate physics majors. Statistical and quantum physics are presented in great mathematical detail, showing the intermediary steps in the most important calculations. Special relativity, however, is treated in a very short chapter that lacks depth and application. Very useful are the large collections of problems presented at the ends of the chapters. Being aware of the more supplementary (for mathematical rigor) nature of their contribution, the authors suggest the more traditional Modern Physics by Kenneth S. Krane (2nd ed., 1996) for introductory reading. For students who want to learn more about the topics that heralded the modern era of physics. Summing Up: Recommended. Upper-division undergraduates; graduate students. U. Greife Colorado School of Mines

1 Introduction to Special Relativity	p. 1
1.1 Michelson-Morley Experiment and Lorentz Transformations	p. 2
1.2 Relativistic Kinematics	p. 8
Problems	p. 16
2 Introduction to Quantum Physics	p. 29
2.1 The Photoelectric Effect	p. 29
2.2 Bohr's Quantum Theory	p. 34
2.3 De Broglie's Interpretation	p. 36
2.4 Schrodinger's Equation	p. 42
2.4.1 The Uncertainty Principle	p. 46
2.4.2 The Speed of Waves	p. 48
2.4.3 The Collective Interpretation of de Broglie's Waves	p. 49
2.5 The Potential Barrier	p. 49
2.5.1 Mathematical Interlude: Differential Equations with Discontinuous Coefficients	p. 51
2.5.2 The Square Barrier	p. 53
2.6 Quantum Wells and Energy Levels	p. 60
2.7 The Harmonic Oscillator	p. 66
2.8 Periodic Potentials and Band spectra	p. 71
Problems	p. 77
3 Introduction to the Statistical Theory of Matter	p. 93
3.1 Thermal Equilibrium by Gibbs' Method	p. 97
3.1.1 Einstein's Crystal	p. 100
3.1.2 The Particle in a Box with Reflecting Walls	p. 102
3.2 The Pressure and the Equation of State	p. 103
3.3 A Three Level System	p. 105
3.4 The Grand Canonical Ensemble and the Perfect Quantum Gas	p. 108
3.4.1 The Perfect Fermionic Gas	p. 110
3.4.2 The Perfect Bosonic Gas	p. 118
3.4.3 The Photonic Gas and the Black Body Radiation	p. 121
Problems	p. 124
A Quadrivectors	p. 133
B The Schrodinger Equation in a Central Potential	p. 137
C Thermodynamics and Entropy	p. 147
Index	p. 151

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