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

Authors: Masao Hirokawa

Issue: Volume 58 (2009), Issue 4, 1493-1536

Abstract: We study the Dicke-type crossings among eigenvalues of a type of differential operators describing the non-commutative 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.