On spectral problems of discrete Schrödinger operators

Chi-Hua Chan; Po-Chun Huang

Applications of Mathematics (2021)

  • Volume: 66, Issue: 3, page 325-344
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Chan, Chi-Hua, and Huang, Po-Chun. "On spectral problems of discrete Schrödinger operators." Applications of Mathematics 66.3 (2021): 325-344. <http://eudml.org/doc/298036>.

@article{Chan2021,
abstract = {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.},
author = {Chan, Chi-Hua, Huang, Po-Chun},
journal = {Applications of Mathematics},
keywords = {discrete Schrödinger operator},
language = {eng},
number = {3},
pages = {325-344},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On spectral problems of discrete Schrödinger operators},
url = {http://eudml.org/doc/298036},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Chan, Chi-Hua
AU - Huang, Po-Chun
TI - On spectral problems of discrete Schrödinger operators
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 325
EP - 344
AB - 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.
LA - eng
KW - discrete Schrödinger operator
UR - http://eudml.org/doc/298036
ER -

References

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