Geodesic
On spectral problems of discrete Schrödinger operators
Applications of Mathematics, Tome 66 (2021) no. 3, pp. 325-344 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 and largest eigenvalues attain the extrema under certain constraints by use of the notion of generalized directional derivative and the method of Lagrange multiplier.
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 and largest eigenvalues attain the extrema under certain constraints by use of the notion of generalized directional derivative and the method of Lagrange multiplier.
DOI : 10.21136/AM.2021.0203-19
Classification : 34B09
Keywords: discrete Schrödinger operator 
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     title = {On spectral problems of discrete {Schr\"odinger} operators},
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     pages = {325--344},
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Chan, Chi-Hua; Huang, Po-Chun. On spectral problems of discrete Schrödinger operators. Applications of Mathematics, Tome 66 (2021) no. 3, pp. 325-344. doi: 10.21136/AM.2021.0203-19

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