Mathematical Methods XIA

List of Contributors Foreword Preface 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 References 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 ReferencesChapter 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 References 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 References 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 Appendix References 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 References 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 References 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 References Author Index Subject Index