CONSTRUCTION OF INTERPOLANT POLYNOMIALS FOR APPROXIMATING EIGENVALUESOF A HAMILTONIAN WHICH IS DEPENDENT ON A COUPLING PARAMETER

A method for constructing approximate secular polynomials from a limit ed number of perturbation series terms is described. These are polynom ial functions of two variables, the energy and the resonance integral coupling. The polynomials can be solved to give the energy as a functi on of the coupling. Results which were obtained from a number of polyn omials are presented, in particular, values for the energy from relati vely small polynomials which give very good approximations to the ener gy of the infinite chain system they describe. These results are compa red to other methods for obtaining upper and lower bounds for the ener gy of the infinite chain.