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The method is an extension to negative energies of a spectral integralequation method to solve the Schroedinger equation, developed previously forscattering applications. One important innovation is a re-scaling procedure inorder to compensate for the exponential behaviour of the negative energyGreen's function. Another is the need to find approximate energy eigenvalues,to serve as starting values for a subsequent iteration procedure. In order toillustrate 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 bindingenergy, 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 threesignificant figures for the binding energy, and with 320 mesh points theaccuracy increased to six significant figures. An application to a potentialwith two wells separated by a barrier, is also made.Comment: 19 pages, 3 figures, submitted to Eur. J. Phy

An economical method to calculate eigenvalues of the Schrödinger equation