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Asymptotic expansion in time of the Schrödinger group on conical manifolds

Xue Ping Wang (2006)

Annales de l’institut Fourier

For Schrödinger operator P on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of P near zero. Long-time expansion of the Schrödinger group U ( t ) = e - i t P is obtained under a non-trapping condition at high energies.

Charge transfer scatteringin a constant electric field

Lech Zieliński (1999)

Colloquium Mathematicae

We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.

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