Inverse spectral results for Schrödinger operators on the unit interval with potentials in L^P spaces

Abstract

We consider the Schrödinger operator on $[0,1]$ with potential in $L^1$. We prove that two potentials already known on $[a,1]$ ($a\in (0,1/2]$) and having their difference in $L^p$ are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of $p$ (and $a$) showing the role of $p$.