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