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Displaying similar documents to “Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential.”

On spectral problems of discrete Schrödinger operators

Chi-Hua Chan, Po-Chun Huang (2021)

Applications of Mathematics

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A special type of Jacobi matrices, discrete Schrödinger operators, is found to play an important role in quantum physics. In this paper, we show that given the spectrum of a discrete Schrödinger operator and the spectrum of the operator obtained by deleting the first row and the first column of it can determine the discrete Schrödinger operator uniquely, even though one eigenvalue of the latter is missing. Moreover, we find the forms of the discrete Schrödinger operators when their smallest...