Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

L. Boulton, S. A. M. Marcantognini, M. D. Morán

Research output: Contribution to journalArticle

Abstract

We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator HA,B:=B(-∂x 2) + Ax2 acting on L2(ℝ; ℂ2) becomes a three-terms recurrence. Here A and B are 2 x 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of HA,B that lie in the span of the first four elements of this basis when AB ≠ BA.

Original languageEnglish
Pages (from-to)121-131
Number of pages11
JournalLetters in Mathematical Physics
Volume70
Issue number2
DOIs
Publication statusPublished - Nov 2004

Keywords

  • Eigenfunction expansion
  • Higher dimensional Hermite basis
  • Non-commutative harmonic oscillators

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Finite lifetime eigenfunctions of coupled systems of harmonic oscillators'. Together they form a unique fingerprint.

  • Cite this