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We consider the inverse problem of the determining the potential in thedynamical Schr\"odinger equation on the interval by the measurement on thewhole boundary. Provided that source is \emph{generic} using the BoundaryControl method we recover the spectrum of the problem from the observation ateither left or right end points. Using the specificity of the one-dimensionalsituation we recover the spectral function, reducing the problem to theclassical one which could be treated by known methods. We adapt the algorithmto the situation when only the finite number of eigenvalues are known andprovide the result on the convergence of the method.

Reconstructing the potential for the 1D Schr\"odinger equation from boundary measurements