Non-relativistic Quantum Theory

Description

Intro Contents Preface 1 HowDid SchrÂödinger Get His Equation? 2 Heisenbergâ#x80 #x99 s Matrix Mechanics and Diracâ#x80 #x99 s Re-creation of it 3 Diracâ#x80 #x99 s Derivation of the Quantum Conditions 4 The Equivalence between Matrix Mechanics and Wave Mechanics 5 The Dirac Delta Function 6 Why Do We Need Hilbert Space? 7 The Dirac Bra Ket Notation and the Riesz Theorem 8 Self-Adjoint Operators in Hilbert Space 9 The Spectral Theorem, Discrete and Continuous Spectra 10 Coordinate and Momentum Representations of Quantum States, Fourier Transforms 11 The Uncertainty Principle 12 Commutator Algebra 13 Ehrenfestâ#x80 #x99 s Theorem14 The Simple Harmonic Oscillator 15 Complete Set of Commuting Observables 16 Solving SchrÂödingerâ#x80 #x99 s Equation 17 Symmetry, Invariance, and Conservation in Quantum Mechanics 18 Why is Group Theory Useful in Quantum Mechanics? 19 SO(3) and SU(2) 20 The Spectrum of the Angular Momentum Operators 21 Whence the Spherical Harmonics? 22 Irreducible Representations of SU(2) and SO(3), Rotation Matrices 23 Direct Product Representations, Clebsch-Gordon Coefficients 24 Transformations of Wave Functions and Vector Operators under SO(3) 25 Irreducible Tensor Operators and the Wigner-Eckart Theorem26 Reduction of Direct Product Representations of SO(3): The Addition of Angular Momenta 27 The Calculation of Clebsch-Gordon Coe.cients: The 3-j Symbols 28 Applications of the Wigner-Eckart Theorem 29 The Symmetric Groups 30 The Lie Algebra of SO(4) and the Hydrogen Atom 31 Stationary Perturbations 32 The Fine Structure of Hydrogen: Application of Degenerate Perturbation Theory 33 Time-Dependent Perturbation Theory 34 Interaction of Matter with the Classical Radiation Field: Application of Time-Dependent Perturbation Theory 35 Potential Scattering Theory36 Analytic Properties of the S-Matrix: Bound States and Resonances 37 Non-Perturbative Bound-State and Scattering-State Solutions: Radiation-Induced Bound-Continuum Interactions 38 Geometric Phases: The Aharonov-Bohm Effect and the Magnetic Monopole 39 The Berry Phase in Molecular Dynamics 40 The Dynamic Phase: Riemann Surfaces in the Semiclassical Theory of Non-Adiabatic Collisions Homotopy and Homology 41 â#x80 #x9C The Connection is the Gauge Field and the Curvature is the Forceâ#x80 #x9D : Some Differential Geometry 42 Topological Quantum (Chern) Numbers: The Integer Quantum Hall Effect43 de Rham Cohomology and Chern Classes: Some More Differential Geometry 44 Chern-Simons Forms: The Fractional Quantum Hall Effect, Anyons and Knots References Index