# 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.