Page 9 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

Preface ix

ential equation by the series solution method. Ladder operators provide practice
for the student in operations that are used in more advanced quantum theory
and in advanced statistical mechanics. Moreover, they yield the eigenvalues
and eigenfunctions more simply and more directly without the need to
introduce generating functions and recursion relations and to consider asymp-
totic behavior and convergence. Although there is no need to invoke Hermite,
Legendre, and Laguerre polynomials when using ladder operators, these func-
tions are nevertheless introduced in the body of the chapters and their proper-
ties are discussed in the appendices. For traditionalists, the series-solution
method is presented in an appendix.
Chapters 7 and 8 discuss spin and identical particles, respectively, and each
chapter introduces an additional postulate. The treatment in Chapter 7 is
limited to spin one-half particles, since these are the particles of interest to
chemists. Chapter 8 provides the link between quantum mechanics and
statistical mechanics. To emphasize that link, the free-electron gas and Bose±
Einstein condensation are discussed. Chapter 9 presents two approximation
procedures, the variation method and perturbation theory, while Chapter 10
treats molecular structure and nuclear motion.
The ®rst-year graduate course in quantum mechanics is used in many
chemistry graduate programs as a vehicle for teaching mathematical analysis.
For this reason, this book treats mathematical topics in considerable detail,
both in the main text and especially in the appendices. The appendices on
Fourier series and the Fourier integral, the Dirac delta function, and matrices
discuss these topics independently of their application to quantum mechanics.
Moreover, the discussions of Hermite, Legendre, associated Legendre, La-
guerre, and associated Laguerre polynomials in Appendices D, E, and F are
more comprehensive than the minimum needed for understanding the main
text. The intent is to make the book useful as a reference as well as a text.
I should like to thank Corpus Christi College, Cambridge for a Visiting
Fellowship, during which part of this book was written. I also thank Simon
Capelin, Jo Clegg, Miranda Fyfe, and Peter Waterhouse of the Cambridge
University Press for their efforts in producing this book.
Donald D. Fitts