Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

Details Finite lifetime eigenfunctions of coupled systems of harmonic oscillators Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

2004-03-10

arxiv.org/abs/math/0403187v2

Mathematics

Spectral Theory

11 pages, 1 figure. Some typos where corrected in this new version

Scientific paper

10.1007/s11005-004-4291-6

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.

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