8. Matrices in Quantum Mechanics

In the Huckel model of electronic energy levels, described in Chapter 7, the relative electronic energies of \(\pi\) orbitals are calculated on the assumption that each \(\pi\) orbital interacts only with it nearest neighbours. A matrix of interactions was constructed and the eigenvalues and eigenvectors found. In this chapter, problems that are more general are explored and this is done by using a basis set, i.e. a set of wavefunctions that are solutions of a known potential, such as particle in a box,to enable more complex problems to be solved by using combinations of these known wavefunctions to solve the Schroedinger equation for an arbitrary potential whose analytical solution is not forthcoming.