We discuss the spectral properties of the operator on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific nilpotent group of a general analysis proposed by J. Dziubański, A. Hulanicki and J. Jenkins.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-3,
author = {B. Helffer},
title = {The Montgomery model revisited},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {391-400},
zbl = {1207.34110},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-3}
}
B. Helffer. The Montgomery model revisited. Colloquium Mathematicae, Tome 120 (2010) pp. 391-400. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-3/