On the Equivalence of Matrix Differential Operators to Schrödinger Form

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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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  -