Elementary Molecular Quantum Mechanics

2nd Edition

Mathematical Methods and Applications

Print ISBN: 9780444626479
eBook ISBN: 9780444626660
Imprint: Elsevier Science
Published Date: 1st August 2013
Page Count: 1012
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The second edition of Elementary Molecular Quantum Mechanics uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics for students of Chemistry and Physics. This highly readable book teaches in detail the mathematical methodologies needed to perform working applications in molecular quantum mechanics as a preliminary step before applying commercial programmes using quantum chemistry calculations.
This book aims to bridge the gap between the classic Coulson’s Valence, where application of wave mechanical principles to valence theory is presented in a fully non-mathematical way, and McWeeny’s Methods of Molecular Quantum Mechanics, where recent advances in the application of quantum mechanical methods to molecular problems are presented at a research level in a full mathematical way. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each Chapter.

Table of Contents



Part 1: Mathematical Methods

Chapter 1. Mathematical foundations and approximation methods

1.1 Mathematical Foundations

1.2 The Variational Method

1.3 Perturbative Methods for Stationary States

1.4 The Wentzel–Kramers–Brillouin Method

1.5 Problems 1

1.6 Solved Problems

Chapter 2. Coordinate systems

2.1 Introduction

2.2 Systems of Orthogonal Coordinates

2.3 Generalized Coordinates

2.4 Cartesian Coordinates (x,y,z)

2.5 Spherical Coordinates (r,θ,φ)

2.6 Spheroidal Coordinates (μ,ν,φ)

2.7 Parabolic Coordinates (ξ,η,φ)

2.8 Problems 2

2.9 Solved Problems

Chapter 3. Differential equations in quantum mechanics

3.1 Introduction

3.2 Partial Differential Equations

3.3 Separation of Variables

3.4 Solution by Series Expansion

3.5 Solution Near Singular Points

3.6 The One-dimensional Harmonic Oscillator

3.7 The Atomic One-electron System

3.8 The Hydrogen Atom in an Electric Field

3.9 The Hydrogen Molecular Ion H2+

3.10 The Stark Effect in Atomic Hydrogen

3.11 Appendix: Checking the Solutions

3.12 Problems 3

3.13 Solved Problems

Chapter 4. Special functions

4.1 Introduction

4.2 Legendre Functions

4.3 Laguerre Functions

4.4 Hermite Functions

4.5 Hypergeometric Functions

4.6 Bessel Functions

4.7 Functions Defined by Integrals

4.8 The Dirac δ-Function

4.9 The Fourier Transform

4.10 The Laplace Transform

4.11 Spherical Tensors

4.12 Orthogonal Polynomials

4.13 Padé Approximants



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© Elsevier Science 2013
Elsevier Science
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"This interesting book is devoted to both the mathematical methods and applications of Quantum Mechanics in Chemistry...very useful not only for students but for scientists and researchers." --Zentralblatt MATH

"Magnasco presents this detailed quantum chemistry text, building up from basic mathematical foundations to multi-atom systems and molecular vibrations. The first several chapters cover linear algebra, approximation methods, coordinate systems, differential equations, special functions, functions of a complex variable, and matrix mechanics." --ProtoView.com, April 2014