Mathematical Methods in Chemistry and Physics

Mathematics is the language of the physical sciences and is essential for a clear understanding of fundamental scientific concepts. The fortuna te fact that the same mathematical ideas appear in a number of distinct scientific areas prompted the format for this book. The mathematical framework for matrices and vectors with emphasis on eigenvalue-eigenvector concepts is introduced and applied to a number of distinct scientific areas. Each· new application then reinforces the applications which preceded it.
Most of the physical systems studied involve the eigenvalues and eigenvec- tors of specific matrices. Whenever possible, I have selected systems which are described by 2 x 2 or 3 x 3 matrices. Such systems can be solved completely and are used to demonstrate the different methods of solution. In addition, these matrices will often yield the same eigenvectors for different physical systems, to provide a sense of the common mathematical basis of all the problems. For example, an eigenvector with components (1, -1) might describe the motions of two atoms in a diatomic molecule or the orientations of two atomic orbitals in a molecular orbital. The matrices in both cases couple the system components in a parallel manner.