Geometric Quantum Mechanics

ISBN-13: 9781119913214 / Angielski / Twarda / 2023 / 350 str.

van Veenendaal

Spis treści

1 Space1.1 The exponential function1.2 The two-dimensional plane1.3 Calculus and operators1.4 Function space for rotation in a plane1.5 Three-dimensional space1.6 Spinors1.7 Pauli matrices1.8 Rotation matrices1.9 Projections1.10 Function space in three dimensions1.11 Fourier transform and translation1.12 Dual bases1.13 Dual basis obtained via matrix inversion1.14 The unit sphere1.15 Function space for rotation in three dimensions1.16 Higher-order operators1.17 Operator techniques for angular momentum1.18 Chapter summary2 Spacetime2.1 Introduction2.2 The four-vector2.3 Four-momentum for particles2.4 Function space for spacetime2.5 Spacetime spinors2.6 gamma matrices2.7 Motion in an electromagnetic field2.8 Creation of electromagnetic fields: Maxwell's equations2.9 Nonrelativistic limit of Dirac equation2.10 Interactions between particles and electromagnetic field2.11 Spin-orbit coupling2.12 Spin-orbit coupling2.13 Schrödinger/Heisenberg equations and propagators2.14 Electroweak interaction3 Single-particle problems3.1 Introduction3.2 Quantum harmonic oscillator3.3 Perturbed harmonic oscillator3.4 Two-dimensional harmonic oscillator via differential equation3.5 Two-dimensional harmonic oscillator via unit vectors3.6 Radial equation for hydrogen atom3.7 Transitions on atoms3.8 Molecules and solids3.9 Periodic potential in a solid3.10 Scattering from local potential3.11 Single state and a band4 Many-particle systems4.1 Introduction4.2 Wavefunctions for many-body systems4.3 Quantum statistics4.4 The Fermi sea in solids4.5 Tensors4.6 Electon interactions on an atom4.7 Strong interaction: mesons4.8 Strong interaction: baryon4.9 Nuclear structure5 Collective and emergent phenomena5.1 Magnetism5.2 Superconductivity5.3 Mass generation5.4 Symmetry breaking5.5 Screening in solids5.6 Plasmons in solids 5.7 Superfluidity

O autorze

Michel van Veenendaal, PhD is a Distinguished Research Professor in the Department of Physics at Northern Illinois University, DeKalb, IL, USA and a physicist at Argonne National Laboratory, IL, USA.