The $J$-matrix method
Classical Analysis and ODEs
2014-03-13 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0810.4558,
title = {The $J$-matrix method},
author = {Mourad E. H. Ismail and Erik Koelink},
journal= {arXiv preprint arXiv:0810.4558},
year = {2014}
}
Comments
18 pages, title changed, minor changes, to appear in Adv. Appl. Math