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Valleys in Quantum Mechanics

Hideaki Aoyama·Hisashi Kikuchi·Ikuo Okouchi·Masatoshi Sato·Shinya Wada
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Abstract

Conventionally, perturbative and non-perturbative calculations are performed independently. In this paper, valleys in the configuration space in quantum mechanics are investigated as a way to treat them in a unified manner. All the known results of the interplay of them are reproduced naturally. The prescription for separating the non-perturbative contribution from the perturbative is given in terms of the analytic continuation of the valley parameter. Our method is illustrated on a new series of examples with the asymmetric double-well potential. We obtain the non-perturbative part explicitly, which leads to the prediction of the large order behavior of the perturbative series. We calculate the first 200 perturbative coefficients for a wide range of parameters and confirm the agreement with the prediction of the valley method.

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Hideaki Aoyama, Hisashi Kikuchi, Ikuo Okouchi, Masatoshi Sato, Shinya Wada. 1997-10-31. Valleys in Quantum Mechanics. https://doi.org/10.1016/s0370-2693(98)00116-6

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