The J-matrix method

Given an operator L acting on a function space, the J-matrix method consists of finding a sequence yn of functions such that the operator L acts tridiagonally on yn. Once such a tridiagonalization is obtained, a number of characteristics of the operator L can be obtained. In particular, information on eigenvalues and eigenfunctions, bound states, spectral decompositions, etc. can be obtained in this way. We discuss the general set-up and next two examples in detail; the Schrödinger operator with Morse potential and the Lamé equation.