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Decay at infinity of eigenfunctions of Schrödinger operators with polynomial electro-magnetic field. (Décroissance à l’infini des fonctions propres de l’opérateur de Schrödinger avec champ électromagnétique polynomial.) (French) Zbl 0814.35080
This paper concerns the exponential decay at infinity of the eigenfunctions of Schrödinger operators with magnetic field. The electromagnetic potentials are assumed to be polynomials, and the decay is expressed in terms of some “Agmon distance” associated to a positive function involving all the derivatives of both electric and magnetic potentials. A semiclassical version of the result is also given.

35P05 General topics in linear spectral theory for PDEs
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35J10 Schrödinger operator, Schrödinger equation
Full Text: DOI
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