Geometric Quantum Mechanics

1 Space 1.1 The exponential function 1.2 The two-dimensional plane 1.3 Calculus and operators 1.4 Function space for rotation in a plane 1.5 Three-dimensional space 1.6 Spinors 1.7 Pauli matrices 1.8 Rotation matrices 1.9 Projections 1.10 Function space in three dimensions 1.11 Fourier transform and translation 1.12 Dual bases 1.13 Dual basis obtained via matrix inversion 1.14 The unit sphere 1.15 Function space for rotation in three dimensions 1.16 Higher-order operators 1.17 Operator techniques for angular momentum 1.18 Chapter summary 2 Spacetime 2.1 Introduction 2.2 The four-vector 2.3 Four-momentum for particles 2.4 Function space for spacetime 2.5 Spacetime spinors 2.6 γ matrices 2.7 Motion in an electromagnetic field 2.8 Creation of electromagnetic fields: Maxwell’s equations 2.9 Nonrelativistic limit of Dirac equation 2.10 Interactions between particles and electromagnetic field 2.11 Spin-orbit coupling 2.12 Spin-orbit coupling 2.13 Schrödinger/Heisenberg equations and propagators 2.14 Electroweak interaction 3 Single-particle problems 3.1 Introduction 3.2 Quantum harmonic oscillator 3.3 Perturbed harmonic oscillator 3.4 Two-dimensional harmonic oscillator via differential equation 3.5 Two-dimensional harmonic oscillator via unit vectors 3.6 Radial equation for hydrogen atom 3.7 Transitions on atoms 3.8 Molecules and solids 3.9 Periodic potential in a solid 3.10 Scattering from local potential 3.11 Single state and a band 4 Many-particle systems 4.1 Introduction 4.2 Wavefunctions for many-body systems 4.3 Quantum statistics 4.4 The Fermi sea in solids 4.5 Tensors 4.6 Electon interactions on an atom 4.7 Strong interaction: mesons 4.8 Strong interaction: baryon 4.9 Nuclear structure 5 Collective and emergent phenomena 5.1 Magnetism 5.2 Superconductivity 5.3 Mass generation 5.4 Symmetry breaking 5.5 Screening in solids 5.6 Plasmons in solids 5.7 Superfluidity