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List of Contributors

Foreword

Preface

Contents of Previous Volumes

Chapter 9 / Methods in Lattice Statistics

I. Introduction

II. Concepts in Graph Theory

III. Evaluation of Lattice Constants

IV. Exact Series Expansions

V. The Dimer Problem

VI. Pfaffian Solution of the Planar Ising Problem

Appendix—Methods of Series Analysis

References

Chapter 10 / Probability Theory and Stochastic Processes

I. Introduction

II. Random Variables and Probability Distributions

III. Functions of Random Variables

IV. Stochastic Processes—General

V. Stochastic Processes Discrete in Both Sample Space and Time

VI. Stochastic Processes Discrete in Sample Space but Continuous in Time

VII. Stochastic Processes Continuous in Both Sample Space and Time

References

Chapter 11 / Nonequilibrium Problems—Projection Operator Techniques

I. Introduction

II. The Projection Operator Technique

III. Brownian Motion

IV. Further Applications—Lowest Order Results

V. Higher Order Results

References

Chapter 12 / Scattering Theory

I. Introduction

II. Simple Particle Scattering from a Fixed Center

III. The Green's Function and Solutions to an Inhomogeneous Differential Equation

IV. Elastic Scattering from Atoms

V. Inelastic Scattering

VI. The Multichannel Scattering Matrix

VII. Approximate Wave Functions

VIII. Autoionization

IX. The Optical Model

X. The R-Matrix Theory

References

Chapter 13 / The Solution of Integral and Differential Equations

I. Introduction

II. Theory of Operator Equations—Fundamentals

III. Integral Equations: Linear and Nonlinear

IV. Differential Equations, Mainly Nonlinear

V. Methods of Solution

References

Author Index

Subject Index

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1st Edition - January 1, 1975

Editor: Douglas Henderson

Language: EnglisheBook ISBN:

9 7 8 - 0 - 3 2 3 - 1 4 7 6 9 - 9

Physical Chemistry: An Advanced Treatise, Volume XIB: Mathematical Methods focuses on mathematical techniques that consist of concepts relating to differentiation and integration.… Read more

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Physical Chemistry: An Advanced Treatise, Volume XIB: Mathematical Methods focuses on mathematical techniques that consist of concepts relating to differentiation and integration. This book discusses the methods in lattice statistics, Pfaffian solution of the planar Ising problem, and probability theory and stochastic processes. The random variables and probability distributions, non-equilibrium problems, Brownian motion, and scattering theory are also elaborated. This text likewise covers the elastic scattering from atoms, solution of integral and differential equations, concepts in graph theory, and theory of operator equations. This volume provides graduate and physical chemistry students a basic understanding of mathematical techniques important in chemistry.

List of Contributors

Foreword

Preface

Contents of Previous Volumes

Chapter 9 / Methods in Lattice Statistics

I. Introduction

II. Concepts in Graph Theory

III. Evaluation of Lattice Constants

IV. Exact Series Expansions

V. The Dimer Problem

VI. Pfaffian Solution of the Planar Ising Problem

Appendix—Methods of Series Analysis

References

Chapter 10 / Probability Theory and Stochastic Processes

I. Introduction

II. Random Variables and Probability Distributions

III. Functions of Random Variables

IV. Stochastic Processes—General

V. Stochastic Processes Discrete in Both Sample Space and Time

VI. Stochastic Processes Discrete in Sample Space but Continuous in Time

VII. Stochastic Processes Continuous in Both Sample Space and Time

References

Chapter 11 / Nonequilibrium Problems—Projection Operator Techniques

I. Introduction

II. The Projection Operator Technique

III. Brownian Motion

IV. Further Applications—Lowest Order Results

V. Higher Order Results

References

Chapter 12 / Scattering Theory

I. Introduction

II. Simple Particle Scattering from a Fixed Center

III. The Green's Function and Solutions to an Inhomogeneous Differential Equation

IV. Elastic Scattering from Atoms

V. Inelastic Scattering

VI. The Multichannel Scattering Matrix

VII. Approximate Wave Functions

VIII. Autoionization

IX. The Optical Model

X. The R-Matrix Theory

References

Chapter 13 / The Solution of Integral and Differential Equations

I. Introduction

II. Theory of Operator Equations—Fundamentals

III. Integral Equations: Linear and Nonlinear

IV. Differential Equations, Mainly Nonlinear

V. Methods of Solution

References

Author Index

Subject Index

- No. of pages: 508
- Language: English
- Edition: 1
- Published: January 1, 1975
- Imprint: Academic Press
- eBook ISBN: 9780323147699

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