Reconstructing the potential for the one-dimensional Schrodinger equation from boundary measurements

We consider the inverse problem of determining the potential in the dynamical Schrodinger equation on the interval by the measurement on the boundary. We use the boundary control method to recover the spectrum of the problem from the observation at either left or right endpoints. Using the specificity of the one-dimensional situation, we recover the spectral function, reducing the problem to the classical one which could be treated by known methods. We apply the algorithm to the situation when only a finite number of eigenvalues are known and prove the convergence of the method.