Double wells: Perturbation series summable to the eigenvalues and directly computable approximations. (English) Zbl 0645.35071

We give a rigorous proof of the analyticity of the eigenvalues of the double-well Schrödinger operators and of the associated resonances. We specialize the Rayleigh-Schrödinger perturbation theory to such problems, obtaining an expression for the complex perturbation series uniquely related to the eigenvalues through a summation method. By an approximation we obtain new series expansions directly computable, still summable, which, in the case of the Herbst-Simon model, can be given in an explicit form.


35P05 General topics in linear spectral theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
35B20 Perturbations in context of PDEs
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