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



No. of pages:
© 2013
Elsevier Science
eBook ISBN:
Print ISBN:


"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.", April 2014