We construct approximate solutions to the time--dependent Schr\" odinger equation $ i\hbar
(\partial\psi)/(\partial t)=-(\hbar^ 2)/2\Delta\psi+ V\psi $ for small values of $\hbar $. If $ V …

It is known that for n≥ 3 centres and positive energies the n-centre problem of celestial
mechanics leads to a flow with a strange repellor and positive topological entropy. Here we …

Let H 0 be a self-adjoint operator in some Hilbert space H, and let λ 0 be a (possibly
degenerate) eigenvalue of H 0 embedded in its essential spectrum σ ess (H 0) with …

This paper adapts the techniques of exponential weighted phase space estimates as
studied in Refs. 1–4 to a case where there is no analyticity, but regularity in the sense of …

Semiclassical Dynamics and Exponential Asymptotics Page 1 Semiclassical Dynamics and
Exponential Asymptotics George A. Hagedorn and Alain Joye Abstract. We discuss various …

A one-degree-of-freedom oscillatory Hamiltonian system with a parameter depending
singularly on the slow time is considered. It is shown that the system possesses an adiabatic …

In quantum mechanics the temporal decay of certain resonance states is associated with an
effective time evolution e− ith (κ), where h (·) is an analytic family of non-self-adjoint matrices …