Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

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

doi:10.1007/s11005-004-4291-6

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 journal › Article › peer-review

Abstract

We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator H_A,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 H_A,B that lie in the span of the first four elements of this basis when AB ≠ BA.

Original language	English
Pages (from-to)	121-131
Number of pages	11
Journal	Letters in Mathematical Physics
Volume	70
Issue number	2
DOIs	https://doi.org/10.1007/s11005-004-4291-6
Publication status	Published - Nov 2004

Keywords

Eigenfunction expansion
Higher dimensional Hermite basis
Non-commutative harmonic oscillators

ASJC Scopus subject areas

General Physics and Astronomy
Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s11005-004-4291-6

Cite this

@article{9b0b038b74224024b90ad0f9c0a68c44,

title = "Finite lifetime eigenfunctions of coupled systems of harmonic oscillators",

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.",

keywords = "Eigenfunction expansion, Higher dimensional Hermite basis, Non-commutative harmonic oscillators",

author = "L. Boulton and Marcantognini, {S. A. M.} and Mor{\'a}n, {M. D.}",

year = "2004",

month = nov,

doi = "10.1007/s11005-004-4291-6",

language = "English",

volume = "70",

pages = "121--131",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

AU - Boulton, L.

AU - Marcantognini, S. A. M.

AU - Morán, M. D.

PY - 2004/11

Y1 - 2004/11

N2 - 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.

AB - 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.

KW - Eigenfunction expansion

KW - Higher dimensional Hermite basis

KW - Non-commutative harmonic oscillators

UR - http://www.scopus.com/inward/record.url?scp=12444266885&partnerID=8YFLogxK

U2 - 10.1007/s11005-004-4291-6

DO - 10.1007/s11005-004-4291-6

M3 - Article

AN - SCOPUS:12444266885

SN - 0377-9017

VL - 70

SP - 121

EP - 131

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2

ER -

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this