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Stark resonances: Asymptotics and distributional Borel sum. (English) Zbl 0785.35082

Summary: We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by distributional Borel sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the “resonances” of the anharmonic and double well oscillators.

MSC:

35Q40 PDEs in connection with quantum mechanics
81Q15 Perturbation theories for operators and differential equations in quantum theory
35P05 General topics in linear spectral theory for PDEs
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