Spectral asymptotics for Schrödinger operators with a degenerate potential
Françoise Truc (2001-2002)
Séminaire de théorie spectrale et géométrie
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Françoise Truc (2001-2002)
Séminaire de théorie spectrale et géométrie
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We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.