Mathematical Methods XIA

Mathematical Methods XIA

1st Edition - January 28, 1975

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  • Editor: Douglas Henderson
  • eBook ISBN: 9780323145176

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Physical Chemistry: An Advanced Treatise: Mathematical Methods, Volume XIA, is devoted to mathematical techniques of interest to chemists. The purpose of this treatise is to present a comprehensive treatment of physical chemistry for advanced students and investigators in a reasonably small number of volumes. An attempt has been made to include all important topics in physical chemistry together with borderline subjects which are of particular interest and importance. The book begins with discussions of elementary concepts such as linear vector spaces; generalized function theory; complex variable theory; boundary-value problems; approximating functions and their applications in numerical differentiation, integration, and the solution of differential equations; and group theory. These are followed by more advanced and specialized chapters that emphasize chemical applications rather than mathematical rigor. This book provides the student of physical chemistry with a basic understanding of those additional mathematical techniques which are important in chemistry and should enable him to read the current literature in theoretical chemistry.

Table of Contents

  • List of Contributors



    Contents of Previous and Future Volumes

    Chapter 1 / Linear Vector Spaces

    I. Introduction: Vectors in the Physical Sciences

    II. Linear Vector Spaces

    III. Example: Three-Dimensional Euclidean Vectors—I

    IV. Vector Transformations

    V. Matrices

    VI. Example: Three-Dimensional Euclidean Vectors—II

    VII. Vector Spaces of Infinite Dimension


    Chapter 2 / Generalized Functions

    I. Introduction

    II. Definitions

    III. The Algebra of Generalized Functions

    IV. The Calculus of Generalized Functions

    V. Some Singular Generalized Functions

    VI. Fourier Transforms

    VII. Laplace Transforms

    VIII. Conclusion


    Chapter 3/Complex Variable Theory

    I. Introduction

    II. Complex Numbers

    III. Analytic Functions of a Complex Variable

    IV. Complex Integration

    V. Power Series

    VI. Elementary Functions

    VII. Evaluation of Real Definite Integrals

    VIII. Higher Transcendental Functions

    IX. On Fourier Transforms

    X. Quantum Chemistry Integrals

    XI. A Formula of Lagrange and Nondegenerate Perturbation Theory


    Chapter 4 / Boundary-Value Problems

    I. Introduction

    II. Some Typical Boundary-Value Problems

    III. The D'Alembert Solution of the Wave Equation

    IV. Separation of Variables

    V. Eigenvalues, Eigenfunctions, and Expansion Problems

    VI. Boundary-Value Problems in Cylindrical Coordinates

    VII. Boundary-Value Problems in Spherical Coordinates

    VIII. Green's Functions

    IX. Laplace Transform Methods

    X. Conformal Mapping


    Chapter 5 / Numerical Analysis

    I. Introduction

    II. Approximation by Polynomial Interpolation

    III. Approximation by Spline Interpolation

    IV. Approximation by Least Squares

    V. Numerical Differentiation

    VI. Approximate Integration or Quadrature

    VII. Differential Equations

    VIII. Equations in a Single Unknown

    IX. Systems of Linear Equations

    X. Special Methods for Solving Sparse Sets of Equations



    Chapter 6 / Group Theory

    I. Introduction

    II. Definitions

    III. Symmetry Operators

    IV. Group Representation Theory

    V. Some Applications in Molecular Quantum Mechanics

    VI. The Permutation Group and Spin

    VII. Continuous Groups

    VIII. Group Theory and the Solid State


    Chapter 7 / Density Matrices

    I. Introduction

    II. The Full Density Matrix

    III. The Reduced Density Matrix

    IV. The N-Representability Problem

    V. The Single-Particle Reduced Density Matrix

    VI. The Second-Order Reduced Density Matrix

    VII. General Geminal Wave Functions

    VIII. Condensation Phenomena


    Chapter 8 / The Green's Function Method

    I. Introduction

    II. Double-Time Temperature-Dependent Green's Functions

    III. Spectral Representations

    IV. Properties of the Green's Functions

    V. The Reaction of a System to an External Perturbation

    VI. Calculation of the Green's Functions

    VII. Charge-Transfer Spectra of Molecular Crystals

    VIII. Perturbation Theory for the Green's Functions


    Author Index

    Subject Index

Product details

  • No. of pages: 588
  • Language: English
  • Copyright: © Academic Press 1975
  • Published: January 28, 1975
  • Imprint: Academic Press
  • eBook ISBN: 9780323145176

About the Editor

Douglas Henderson

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