ABSTRACT
As in classical mechanics the number of exactly soluble quantum mechanical problems is very limited and in most cases of practical interest numerical techniques and approximation methods are unavoidable. The availability of fast computers has turned quantum computation into a major industry. This chapter looks at the several approximation techniques. In seeking to solve the Schrodinger equation with the perturbed Hamiltonian, it is convenient to work with series expansions by introducing a dimensionless parameter λ. In many cases the system of interest differs from an exactly soluble system by only a small disturbance, enabling an approximation to be made by expanding in powers of a smallness parameter. The Variational Method provides a very simple method of approximating energy eigenvalues. It is most useful for computing ground state energies and its success depends on our being able to make a reasonable guess for the form of the ground state wave function.
