廣義相對論

Quantum Mechanics   Peter J. Olver

第一章 Hamiltonian Mechanics

(1)Hamiltonian Systems   (2)Poisson Brackets   (3)Symmetry and First Integrals   (4)Hamiton-Jacobi Theory

第 二章 Geometric Optics and Wave Mechanics

(1)The Wave Equation   (2)Maxwell Wquation   (3)High Frequency Limit and Quantization

第三章 Basics of Quantum Mechanicsr

(1)Phase space   (2)Observable   (3)Schrodinger Equation   (4)Spectrum   (5)The Uncertainty Principle

第四章 Linear Operators and Spetrum

(1)Hilbert Space and Linear Operator   (2)The Spectral Theorem   (3)Spectrum of Operators   (4)Dispersion and Stationary Phase

第五章 One-dimensional Problems

(1)The Harmonic Oscillator   (2)Scattering and Inverse Sacttering   (3)Isopectral Flows

第六章 Symmetry in Quantum Mechanics

(1)Group Repersentations   (2)Lie Algebra Representations   (3)Representations of the Orthogonal Group   (4)The Hydrogen Atom   (5)The Zeeman Effect  (6)Addition of Angular Moments

(7)Intensities and Selection Rules   (8)Parity   (9)Systems of Identical Particles   (10)Representation Theory of Finite Groups   (11)Representations of the Symmetric Group

(12)Symmetry Classes of Tensors   (13)Tensor Products   (14)Plethysm   (15)Orbital-Spin and Total Amgular Momentum Coupling

第七章 Relativistic Quantum Mechanics

(1)The Lorentz Group    (2)The Dirac Equation   (3)Clifford Algebra   (4)Clifford Groups and Spinors   (5)Reprsesentations of the Lorentz Group   (6)Relativistic Spinors   

(7)Lorentz-Invariant Equations   (8)Symmetries of the Dirac Equation   (9)Relativistic Spin   (10)Particle in an Electromagnetic Field   (11)Solutions of the Dirac Equation   

(12)Spherically Symmetric Potential   (13)Non-relativistic Limit

1. The Geometry of Spacetime                     James J. Callahan   習作  勘誤   Errata for the Solutions   [ResearchGate]
2. General Relativity for Mathematicians      Rainer K. Sachs   H.Wu(伍鴻熙)
3. Relativity :(1) the special theory   (2) the general theory      J.L.Synge