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.
- Eigenfunction expansion
- Higher dimensional Hermite basis
- Non-commutative harmonic oscillators
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics