Determining the potential in the Schrödinger equation from the Dirichlet to Neumann map by the boundary control method

We consider the problem of identifying the potential in the one-dimensional Schrödinger equation with input Dirichlet data, from measured Neumann data. Knowledge of the Dirichlet to Neumann map together with spectral controllability results for the Schrödinger equation obtained using properties of exponential Riesz bases allow recovery of the spectral data. Once the the spectral data is recovered, we use the Boundary Control method to solve the identification problem.