A recursion equation for computing the total reflectance amplitude from a given potential is derived. It is shown that the poles of the total reflectance amplitude are the bound eigenvalues of the problems. The method avoids complicated boundary value problems usually encountered in computing the bound eigenvalues of the Schrödinger equation. The utility of the method is demonstrated by two examples. A simple algorithm for the numerical approach is derived. Finally the physical meaning in terms of standing waves is discussed.