2000 Mathematics Subject Classification: 81Q60, 35Q40.
A standard supersymmetric quantum system is defined by a Hamiltonian [^H] = ½([^Q]*[^Q] +[^Q][^Q]*), where the super-charge [^Q] satisfies [^Q]2 = 0, [^Q] commutes with [^H]. So we have [^H] ≥ 0 and the quantum spectrum of [^H] is non negative. On the other hand Pais-Ulhenbeck proposed in 1950 a model in quantum-field theory where the d'Alembert operator [¯] = [(∂2)/( ∂t2)] − Δx is replaced by fourth order operator [¯]([¯] + m2),...
We study the semi-classical asymptotic behavior as of scattering amplitudes for Schrödinger operators . The asymptotic formula is obtained for energies fixed in a non-trapping energy range and also is applied to study the low energy behavior of scattering amplitudes for a certain class of slowly decreasing repulsive potentials without spherical symmetry.
Dans cet article nous généralisons les résultats obtenus par J. Chazarain sur le spectre d’opérateurs de Schrödinger lorsque . Nous étendons ses résultats aux opérateurs pseudo-différentiels globalement elliptiques d’ordre .
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