A HOCHSTADT-LIEBERMAN THEOREM FOR THE HYDROGEN ATOM EQUATION

Abstract

A spectral analysis of the Sturm-Liouville equation defined on (0,1], and the singularity of type 2/r + l(l + 1)/r(2) at zero is investigated (where l is a positive integer or zero). It is known that the potential function q (r) in the singular Sturm-Liouville problem can be uniquely determined from two spectrums. In this study, we show that if q (r) is prescribed on (1/2, 1], then only one spectrum is sufficient to determine q (r) on the interval (0, 1/2).