The $J$-matrix method

Details The $J$-matrix method The $J$-matrix method

2008-10-24

arxiv.org/abs/0810.4558v2

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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.

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