We will look at two quite different problems to recover the potential in a second order differential operator from information on its spectrum. The first concerns the classical equation with (say) the boundary condition . At the other end point, . This problem has complex eigenvalues and we will show that a single such spectrum suffices to determine .
In the second problem we have the equation
with fixed conditions at and boundedness at . We examine the conjecture that two complete spectra
and for equals two distinct values , is sufficient to determine .