Mathematics for Quantum Chemistry

This concise volume offers undergraduates an introduction to the mathematical formalism encountered in problems of molecular structure and motion. The author presents only four main topics: the calculus of orthogonal functions, the algebra of vector spaces, and the Lagrangian and Hamiltonian formulation of classical mechanics and its applications to molecular motion. These topics possess particular relevance to modern quantum chemistry, especially in regard to the application of quantum mechanics to molecular spectroscopy. Prerequisites include a knowledge of calculus through partial derivatives and multiple integration, and a year of physics and physical chemistry. 1966 ed. Problems. Answers. Index. 13 figures.

Preface,

iii

1 Introduction,

1

(5)

1-1 EIGENVALUE PROBLEMS IN QUANTUM MECHANICS

1

(3)

1-2 EIGENVALUE PROBLEMS IN CLASSICAL MECHANICS

4

(1)

1-3 SCOPE OF THIS BOOK

4

(1)

PROBLEM

5

(1)

2 Orthogonal Functions,

6

(42)

2-1 INTRODUCTORY CONCEPTS: ORTHOGONALITY AND NORMALIZATION

6

(9)

2-2 EXPANSION IN TERMS OF ORTHONORMAL FUNCTIONS

15

(6)

2-3 THE FOURIER SERIES

21

(6)

2-4 CONSTRUCTION OF ORTHONORMAL FUNCTIONS

27

(5)

2-5 THE LEGENDRE POLYNOMIALS AND OTHER SPECIAL FUNCTIONS

32

(13)

PROBLEMS

45

(3)

3 Linear Algebra,

48

(57)

3-1 INTRODUCTION

48

(9)

3-2 MATRICES, DETERMINANTS, AND LINEAR EQUATIONS

57

(19)

3-3 LINEAR TRANSFORMATIONS

76

(8)

3-4 LINEAR OPERATORS

84

(17)

PROBLEMS

101

(4)

4 Classical Mechanics,

105

(31)

4-1 INTRODUCTION AND THE CONSERVATION LAWS

105

(5)

4-2 GENERALIZED COORDINATES AND LAGRANGE'S EQUATIONS; HAMILTON'S EQUATIONS

110

(11)

4-3 VIBRATIONS OF A MECHANICAL SYSTEM

121

(8)

4-4 ROTATIONS OF A RIGID MECHANICAL SYSTEM

129

(5)

PROBLEMS

134

(2)

5 Conclusion,

136

(7)

5-1 THE BRIDGE BETWEEN CLASSICAL AND QUANTUM MECHANICS

136

(4)

5-2 THE SYNTHESIS OF MATRIX AND WAVE MECHANICS

140

(2)

PROBLEMS

142

(1)

Appendix Mathematical Background and Bibliography,

143

(4)

A-1 COMPLEX NUMBERS

143

(1)

A-2 CALCULUS: PARTIAL DERIVATIVES

144

(1)

A-3 BIBLIOGRAPHY

145

(2)

Answers to Problems,

147

(4)

Index,

151

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Mathematics for Quantum Chemistry

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