On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis

摘要

A localization and "cardinality" property, along with a multiplicity result, of the spectrum of certain 2 x 2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator called non-commutative harmonic oscillators, will be described here. The basic tool is the study of a semiclassical reference system.