  The method is an extension to negative energies of a spectral integral
equation method to solve the Schroedinger equation, developed previously for
scattering applications. One important innovation is a re-scaling procedure in
order to compensate for the exponential behaviour of the negative energy
Green's function. Another is the need to find approximate energy eigenvalues,
to serve as starting values for a subsequent iteration procedure. In order to
illustrate the new method, the binding energy of the He-He dimer is calculated,
using the He-He TTY potential. In view of the small value of the binding
energy, the wave function has to be calculated out to a distance of 3000 a.u.
Two hundred mesh points were sufficient to obtain an accuracy of three
significant figures for the binding energy, and with 320 mesh points the
accuracy increased to six significant figures. An application to a potential
with two wells separated by a barrier, is also made.
