Numerical solution of the inverse spectral problem for Bessel operators

Abstract

We consider some inverse spectral problems associated with the singular Sturm–Liouville equation − u ″ + ( q ( x ) + ℓ ( ℓ + 1 ) x 2 ) u = λ u 0 < x < 1 for ℓ = 1 , 2 … , which is obtained by separation of variables in the 3D radial Schrödinger equation. One approach to such problems involves the use of almost isospectral transformations, by means of which a reduction to a similar problem in the classical ℓ = 0 case is possible. In this paper we focus on the development of computational techniques suggested by these ideas.