The Dicke-type crossings among eigenvalues of differential operators in a class of non-commutative oscillators

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Abstract

We study the Dicke-type crossings among eigenvalues of a type of differential operators describing the noncommutative oscillator in a class. This class consists of some matrix-valued Schrödinger operators. We will show how the crossings occur for the differential operators in detail. In particular, we are interested in the crossing between the ground state energy and an excited state energy.

Original languageEnglish
Pages (from-to)1493-1535
Number of pages43
JournalIndiana University Mathematics Journal
Volume58
Issue number4
DOIs
Publication statusPublished - Oct 8 2009

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Differential operator
Eigenvalue
Ground State Energy
Excited States
Operator
Energy
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "We study the Dicke-type crossings among eigenvalues of a type of differential operators describing the noncommutative oscillator in a class. This class consists of some matrix-valued Schr{\"o}dinger operators. We will show how the crossings occur for the differential operators in detail. In particular, we are interested in the crossing between the ground state energy and an excited state energy.",
author = "Masao Hirokawa",
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