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
