Semiclassical Resolvent Estimates Research Articles

On the Born-Oppenheimer approximation of wave operators in molecular scattering theory

In this paper we study the diatomic molecular scattering by reducing the number of particles through Born-Oppenheimer approximation. Under a non-trapping assumption on the effective potential of the molecular Hamiltonian we use semiclassical resolvent estimates to show that non-adiabatic corrections to the adiabatic (or Born-Oppenheimer) wave operators are small. Furthermore we study the classical limit of the adiabatic wave operators by computing its action on quantum observables microlocalized by use of coherent states.

Semiclassical resolvent estimates for N-body Schrödinger operators

In this paper we prove for a generalized N-body Schrödinger operator that the non-trapping condition on the classical hamiltonian and all classical subhamiltonians is both necessary and sufficient for obtaining good semiclassical bounds on the boundary values of the resolvent and their energy derivatives. We accomplish this by generalizing Gérard's geometrical construction of an escape function for three-body problems to N-body problems.

Semiclassical resolvent estimates for the barrier top energy

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Semiclassical resolvent estimates for two and three–body schrödinger operators

We prove uniform resolvent estimates for semiclassical three–body Schrodinger operators under a non–trapping condition for the classical flow of all subsystems. We also prove resolvent estimates for two–body Schrodinger operators with positive potentials when the energy level and the Planck constant tend both to zero.

Semiclassical resolvent estimates for two and three-body Schrödinger operators

We prove uniform resolvent estimates for semiclassical three–body Schrodinger operators under a non–trapping condition for the classical flow of all subsystems. We also prove resolvent estimates for two–body Schrodinger operators with positive potentials when the energy level and the Planck constant tend both to zero.