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The Montgomery model revisited

B. Helffer — 2010

Colloquium Mathematicae

We discuss the spectral properties of the operator ( α ) : = - d ² / d t ² + ( 1 / 2 t ² - α ) ² 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...

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