  In this paper, we investigate the three-dimensional Schrodinger operator with
a periodic, relative to a lattice {\Omega} of R3, potential q. A special class
V of the periodic potentials is constructed, which is easily and constructively
determined from the spectral invariants. First, we give an algorithm for the
unique determination of the potential q in V of the three-dimensional
Schrodinger operator from the spectral invariants that were determined
constructively from the given Bloch eigenvalues. Then we consider the stability
of the algorithm with respect to the spectral invariants and Bloch eigenvalues.
Finally, we prove that there are no other periodic potentials in the set of
large class of functions whose Bloch eigenvalues coincides with the Bloch
eigenvalues of q in V.
