On spectrum of Hermitizable tridiagonal matrices

This paper is devoted to the study on the spectrum of Hermitizable tridiagonal matrices. As an illustration of the application of the author’s recent results on Hermitizable matrices, an explicit criterion for discrete spectrum of the matrices is presented, with a slight and technical restriction. T...

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Bibliographic Details
Published inFrontiers of mathematics in China Vol. 15; no. 2; pp. 285 - 303
Main Author Chen, Mu-Fa
Format Journal Article
LanguageEnglish
Published Beijing Higher Education Press 01.04.2020
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Quantum mechanics
Research Article
isospectral matrices
Hermitizable
birth-death matrix
discrete spectrum
60J27
15B57
81Q10
15A18
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Summary:This paper is devoted to the study on the spectrum of Hermitizable tridiagonal matrices. As an illustration of the application of the author’s recent results on Hermitizable matrices, an explicit criterion for discrete spectrum of the matrices is presented, with a slight and technical restriction. The problem is well known, but from the author’s knowledge, it has been largely opened for quite a long time. It is important in various application, in quantum mechanics for instance. The main tool to solve the problem is the isospectral technique developed a few years ago. Two alternative constructions of the isospectral operator are presented; they are helpful in theoretical analysis and in numerical computations, respectively. Some illustrated examples are included.
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-020-0832-2