Communications in Mathematical Physics

, Volume 279, Issue 2, pp 285–308

On the Spectrum of Certain Non-Commutative Harmonic Oscillators and Semiclassical Analysis

Authors

    • Department of MathematicsUniversity of Bologna
Article

DOI: 10.1007/s00220-008-0436-2

Cite this article as:
Parmeggiani, A. Commun. Math. Phys. (2008) 279: 285. doi:10.1007/s00220-008-0436-2

Abstract

A localization and “cardinality” property, along with a multiplicity result, of the spectrum of certain 2 × 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.

Copyright information

© Springer-Verlag 2008