I Fundamental Physics
1 Principles of Quantum Mechanics
1.1 Wave-particle duality . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Wavelength of a free particle in terms of its energy . . . . . . 11
1.3 Energy quantization . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Radiation spectrum of Hydrogen . . . . . . . . . . . . . . . . 13
1.5 The wave function . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 The wave function of a free particle . . . . . . . . . . . . . . . 16
1.7 Schrödinger's equation . . . . . . . . . . . . . . . . . . . . . . 17
1.7.1 Time-dependent Schrödinger's equation . . . . . . . . . 17
1.7.2 Time-independent Schrödinger's equation . . . . . . . . 19
1.8 Probabilistic interpretation and collapse of the wave function . . . 19
1.9 The many-particle wave function . . . . . . . . . . . . . . . . 22
1.10 Electron states in a Hydrogen atom . . . . . . . . . . . . . . . 22
1.11 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.12 Degeneracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.13 Indistinguishability of quantum particles . . . . . . . . . . . . 24
1.14 Spin-statistics theorem . . . . . . . . . . . . . . . . . . . . . . 25
1.15 Pauli's exclusion principle . . . . . . . . . . . . . . . . . . . . 26
1.16 Appendix. A crash course in complex numbers . . . . . . . . . 26
2 Crystal Structure of Solids
2.1 Periodic table of elements . . . . . . . . . . . . . . . . . . . . 30
2.2 Chemical bonding . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Atomic order in solids . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Bravais lattices . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5 Primitive unit cell . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Crystal basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7 Volume density and atomic packing factor . . . . . . . . . . . 35
2.8 Basic cubic structures . . . . . . . . . . . . . . . . . . . . . . 36
2.9 Formation of diamond structure . . . . . . . . . . . . . . . . . 37
2.10 Miller indices . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.11 Miller indices for cubic structures . . . . . . . . . . . . . . . . 40
2.12 Imperfections and impurities in solids . . . . . . . . . . . . . . 41
3 Equilibrium Statistical Mechanics
3.1 Probability theory . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Microstates and macrostates . . . . . . . . . . . . . . . . . . . 45
3.3 Probabilistic description . . . . . . . . . . . . . . . . . . . . . 46
3.4 Thermodynamic equilibrium . . . . . . . . . . . . . . . . . . . 46
3.5 Postulate of equal a priori probabilities . . . . . . . . . . . . . 47
3.6 Grand canonical distribution . . . . . . . . . . . . . . . . . . . 48
3.7 Fermi-Dirac distribution . . . . . . . . . . . . . . . . . . . . . 50
3.8 Boltzmann approximation . . . . . . . . . . . . . . . . . . . . 52
3.9 Fermi energy at zero temperature . . . . . . . . . . . . . . . . 53
4 Band Theory of Solids
4.1 Electron states in a crystal lattice . . . . . . . . . . . . . . . . 55
4.2 Bloch's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Energy bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Conduction types of solids . . . . . . . . . . . . . . . . . . . . 59
4.4.1 Completely filled bands do not contribute to conductivity 59
4.4.2 Metals and semimetals . . . . . . . . . . . . . . . . . . 60
4.4.3 Dielectrics and semiconductors . . . . . . . . . . . . . 60
4.5 Conduction and valence
The author initially studied at the Faculty of Radio-Physics, Electronics and Computer Systems of the National Taras Shevchenko University of Kyiv, Ukraine, and then at the Department of Physics and Astronomy, York University, Canada. He obtained his PhD in Physics at York University in 2002, after which he did postdoctoral research at Bielefeld University, Germany. He currently holds a position as an Associate Professor in the Department of Physics and Physical Oceanography at the Memorial University of Newfoundland, Canada. He has published papers in non-equilibrium statistical physics, stochastic processes, surface science, biophysics, and semiconductor physics.
