ABSTRACT
Our first discussion of quantum mechanics emphasized the exact solutions of differential equation developed by Schro¨dinger. There are only a few such solutions and the differential equation is finally inadequate; a much more fruitful formulation, especially for molecular systems, was Heisenberg’s [1] version of the theory which made use of representations of operators in matrices. von Neumann [2] reformulated quantum mechanics as an exercise in operator algebra. Matrix algebra and operator algebra are closely analogous. A formulation of quantum mechanics as an application of the linear algebra of matrices is particularly well suited to approximate calculations of electronic structure: it is the practical form of the Roothaan [3] SCF-MO equations. After defining and illustrating the elementary operations of matrices, we
will discuss the diagonalization of matrix representations. This is the most important practical procedure in quantum mechanics’ matrix algebra; learn this concept and you will understand a great deal of quantum chemistry software.
