Letters in Mathematical Physics

, Volume 70, Issue 2, pp 121–131 | Cite as

Finite Lifetime Eigenfunctions of Coupled Systems of Harmonic Oscillators

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


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 \(L^{2}({\mathbb R};\,{\mathbb C}^{2})\) becomes a three-terms recurrence. Here A and B are 2 × 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 ABBA.


non-commutative harmonic oscillators higher dimensional Hermite basis eigenfunction expansion 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • L. Boulton
    • 1
  • S. A. M. Marcantognini
    • 2
  • M. D. Morán
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Departamento de MatemáticasInstituto Venezolano de Investigaciones Cientí ficasCaracasVenezuela
  3. 3.Escuela de Matemáticas, Facultad de CienciasUniversidad Central de VenezuelaCaracasVenezuela

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