A NEW EFFICIENT METHOD FOR CALCULATING PERTURBATION ENERGIES USING FUNCTIONS WHICH ARE NOT QUADRATICALLY INTEGRABLE

A new approach to calculating perturbation energies of bound states ba sed on the use of functions which are not quadratically integrable is suggested. The key to the method is one simple property of the perturb ation equations which, to our knowledge, has not been noticed until kn ow. The use of the resolvent in this method is avoided and the energy spectrum of the unperturbed Hamiltonian is not needed in the calculati on. The resulting method is very simple and straightforward and gives very accurate eigenvalues and wavefunctions.