Perturbation of resonances in quantum mechanics

AbstractSchrödinger operators on L2(R3) of the form −Δ + Vλ with potentials Vλ real-analytic in λ are discussed. The analytic structure in Vλ and k (with k2 the energy variable) of the resolvent kernel, the eigenvalues and resonances is exhibited and we obtain in particular convergent perturbation expansions for the resonances and the corresponding resonance functions. The lower order expansion coefficients are computed explicitly. The resonances and the corresponding functions are also computed for a particle moving under the action of n point interactions. This gives asymptotic low energy information about Schrödinger Hamiltonians with short range potentials. The perturbation theory of resonances, eigenvalues and of the corresponding functions for Hamiltonians describing n point interactions perturbed by a potential is also given