Accuracy on eigenvalues for a Schrödinger operator with a degenerate potential in the semi-classical limit

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Abstract

We consider a semi-classical Schrödinger operator -h2Δ + V with a degenerate potential V(x, y) = f(x)g(y). g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum. We give sharp asymptotic behavior of low eigenvalues bounded by some power of the parameter h, by improving Born-Oppenheimer approximation.

Keywords

Eigenvalues , semi-classical asymptotics , Born-Oppenheimer approximation
  • Abderemane Morame Université de Nantes, Faculté des Sciences, Dpt. Mathématiques, UMR 6629 du CNRS, B.P. 99208, 44322 Nantes Cedex 3, France.
  • Françoise Truc Université de Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, B.P. 74, 38402 St Martin d¨´´´´'Héres Cedex, France.
  • Pages: 1–14
  • Date Published: 2007-08-01
  • Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal

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Published

2007-08-01

How to Cite

[1]
A. Morame and F. Truc, “Accuracy on eigenvalues for a Schrödinger operator with a degenerate potential in the semi-classical limit”, CUBO, vol. 9, no. 2, pp. 1–14, Aug. 2007.

Issue

Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal

Section

Articles