Necessary and sufficient conditions for a system of eigenfunctions and associated functions of a Sturm-Liouville operator with discontinuous coefficients to possess the basis property.
A new method for computation of eigenvalues of the radial Schrödinger operator is presented. The potential is assumed to behave as if and as if . The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function . It is shown that the eigenvalues are the discontinuity points of the function . Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...