Journal of Nonlinear Mathematical Physics

Volume 4, Issue 3-4, September 1997, Pages 278 - 286

On the Equivalence of Matrix Differential Operators to Schrödinger Form

Authors
F. Finkel, N. Kamran
Corresponding Author
F. Finkel
Available Online 1 September 1997.
DOI
10.2991/jnmp.1997.4.3-4.4How to use a DOI?
Abstract

We prove a generalization to the case of s × s matrix linear differential operators of the classical theorem of E. Cotton giving necessary and sufficient conditions for equivalence of eigenvalue problems for scalar linear differential operators. The conditions for equivalence to a matrix Schrödinger operator are derived and formulated geometrically in terms of vanishing conditions on the curvature of a g (s, R)-valued connection. These conditions are illustrated on a class of matrix differential operators of physical interest, arising by symmetry reduction from Dirac's equation for a spinor field minimally coupled with a cylindrically symmetric magnetic field.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
4 - 3-4
Pages
278 - 286
Publication Date
1997/09/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.1997.4.3-4.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - F. Finkel
AU  - N. Kamran
PY  - 1997
DA  - 1997/09/01
TI  - On the Equivalence of Matrix Differential Operators to Schrödinger Form
JO  - Journal of Nonlinear Mathematical Physics
SP  - 278
EP  - 286
VL  - 4
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1997.4.3-4.4
DO  - 10.2991/jnmp.1997.4.3-4.4
ID  - Finkel1997
ER  -