The $J$-matrix method

Abstract

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.

18 pages, title changed, minor changes, to appear in Adv. Appl. Math

References in corpus (4)

• An extended class of L2-series solutions of the wave equation
• The structure relation for Askey-Wilson polynomials
• L2 series solution of the relativistic Dirac-Morse problem for all energies
• Scattering theory with a natural regularization: Rediscovering the J-matrix method