The inverse spectral problem for radial Schrödinger operators on [0,1

We consider an inverse spectral problem for a class of singular Sturm–Liouville operators on the unit interval with explicit singularity a(a+1)/x2, , related to the Schrödinger operator with a radially symmetric potential. The purpose of this paper is the global parametrization of potentials by the spectral data λa and some norming constants κa. For a=0 or 1, λa×κa is already known to be a global coordinate system on . Using some transformation operators, we show that this result holds for any non-negative integer a; moreover, we give a description of the isospectral sets.