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The Montgomery model revisited

100%

Helffer B.

Colloquium Mathematicum

2010

tom 118

nr 2

391-400

We discuss the spectral properties of the operator $𝔥_{ℳ }(α) := -d²/dt² + (1/2 t² - α)²$ 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 nilpotent group of a general analysis proposed by J. Dziubański, A. Hulanicki and J. Jenkins.

Théorèmes d'indice pour des opérateurs différentiels à coefficients polynomiaux

51%

Helffer B., Nourrigat J.

Banach Center Publications

1983

tom 10

nr 1

203-212

Ograniczanie wyników

1 Banach Center Publications

1 Colloquium Mathematicum

2 Helffer B.

1 Nourrigat J.

1 2010

1 1983

Wyniki wyszukiwania

The Montgomery model revisited

Théorèmes d'indice pour des opérateurs différentiels à coefficients polynomiaux