Dynamics A Set of Notes on Theoretical Physical Chemistry

Steen J., Range K., York D.M.

Table of contents :
Properties of vectors and vector space……Page 6
Fundamental operations involving vectors……Page 7
Matrix Operations……Page 11
Unit Matrix……Page 12
More on [A,B]……Page 13
Laplacian expansion……Page 14
Applications of Determinants……Page 15
Generalized Green’s Theorem……Page 16
Symmetric/Antisymmetric Matrices……Page 17
More on Hermitian Matrices……Page 18
Functions of Matrices……Page 19
Unitary……Page 21
Functions and Functionals……Page 22
Functional Derivatives……Page 23
Variational Notation……Page 24
Algebraic Manipulations of Functional Derivatives……Page 25
Generalization to Functionals of Higher Dimension……Page 26
Higher Order Functional Variations and Derivatives……Page 27
Integral Taylor series expansions……Page 28
The chain relations for functional derivatives……Page 29
Homogeneity and convexity……Page 30
Homogeneity properties of functions and functionals……Page 31
Convexity properties of functions and functionals……Page 32
Lagrange Multipliers……Page 34
Part A……Page 35
Part G……Page 36
Part J……Page 37
Part M……Page 38
Newton’s laws……Page 40
Fundamental definitions……Page 41
D’Alembert’s principle……Page 46
Velocity-dependent potentials……Page 49
Frictional forces……Page 50
Variational Principles……Page 54
Hamilton’s Principle……Page 55
Comments about Hamilton’s Principle……Page 56
Conservation Theorems and Symmetry……Page 60
Cartesian Coordinates……Page 61
Generalized Coordinates……Page 62
Classical Viral Theorem……Page 63
Central Force Problem……Page 64
Conditions for Closed Orbits……Page 67
The Kepler Problem……Page 68
The Laplace-Runge-Lenz Vector……Page 71
Introduction……Page 73
Rutherford Scattering in the Laboratory Frame……Page 76
Examples……Page 77
Collisions……Page 78
Elastic Collisions……Page 79
Oscillations……Page 82
1-Dimension……Page 85
Many-Dimension……Page 86
Forced Vibrations……Page 87
Damped Oscillations……Page 88
Fourier Integral Theorem……Page 90
Derivative Theorem Proof……Page 91
Convolution Theorem Proof……Page 92
Parseval’s Theorem Proof……Page 93
Rigid Body Equations of Motion……Page 95
Solving Rigid Body Problems……Page 97
Torque-Free Motion of a Rigid Body……Page 98
Precession in a Magnetic Field……Page 99
Coulomb integrals between Gaussians……Page 100
Fourier Transforms……Page 101
Green’s Function Expansion……Page 103
FFT……Page 104
Fast Fourier Poisson……Page 105
Continuum Dielectric Models……Page 106
Gauss’ Law I……Page 108
Variational Principles of Electrostatics……Page 109
Electrostatics – Recap……Page 110
Dielectrics……Page 112
Exapansions……Page 115
Triangle inequality……Page 116
Schmidt Orthogonalization……Page 117
Expansions of Functions……Page 118
Convergence Theorem for Fourier Series……Page 124
Fourier series for different intervals……Page 128
Complex Form of the Fourier Series……Page 130
Uniform Convergence of Fourier Series……Page 131
Integration of Fourier Series……Page 132
Fourier Integral Representation……Page 135
Fourier Integral Theorem……Page 136
Examples of the Fourier Integral Theorem……Page 139
Parseval’s Theorem for Fourier Transforms……Page 141
Convolution Theorem for Fourier Transforms……Page 142
Fourier Sine and Cosine Transforms and Representations……Page 143