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Caliceti, Emanuela; Grecchi, Vincenzo; Maioli, Marco

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

Commun. Math. Phys. 157, No. 2, 347-357 (1993).
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.

Cited in 6 Documents

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

Keywords:

Oppenheimer-Bender-Wu asymptotics; Stark effect perturbation; bound states; resonances; distributional Borel sum; large order asymptotics of the perturbation coefficients
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\textit{E. Caliceti} et al., Commun. Math. Phys. 157, No. 2, 347--357 (1993; Zbl 0785.35082)
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