Eigenvalue formulas for short-range potentials.

The critical potential parameter T/sub c/ = (Z/sub c/)/sup 1/2/ expressed as a biquadratic function of the nodal and orbital quantum numbers is incorporated into two analytic eigenvalue formulas. The first uses an explicit modification of the Morse-potential eigenvalue formula. The second uses an analytic simplification of the zeroth-order approximation of Imbo, Pagnamenta, and Sukhatme. Both procedures are validated with large sets of eigenvalues obtained by numerical solutions of Schroedinger's equation for three related short-range potentials whose shapes differ widely.