Abstract
Let V i be short range potential and λ i (ϵ) analytic functions. We show that the Hamiltonians H ϵ = − Δ + ϵ −2∑ i = l nλ i( ϵ)V i( (· − x i) ϵ converge in the strong resolvent sense to the point interactions as ϵ → 0, and if V i have compact support then the eigenvalues and resonances of H ϵ, which remains bounded as ϵ → 0, are analytic in ϵ in a complex neighborhood of zero. We compute in closed form the eigenvalues and resonances of H ϵ to the first order in ϵ.
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