Regular two-point boundary value problems for the Schrödinger operator on a path

In this work we study the different type of regular boundary value problems on a path associated with the Schrodinger operator. In particular, we obtain the Green function for each problem and we emphasize the case of Sturm-Liouville boundary conditions. In any case, the Green function is given in terms of second kind Cheby- shev polynomials since they verify a recurrence law similar to the one verified by the Schodinger operator on a path.