Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Issue number2
Publication statusPublished - Nov 2004


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

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Statistical and Nonlinear Physics
  • Mathematical Physics


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