Geodesic
Librations and ground-state splitting in a multidimensional double-well problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 2, pp. 193-205 Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive an asymptotic formula for the splitting of the lowest eigenvalues of the multidimensional Schrödinger operator with a symmetric double-well potential. Unlike the well-known formula of Maslov, Dobrokhotov, and Kolosoltsov, the obtained formula has the form $A(h)e^{-S/h}(1+o(1))$, where $S$ is the action on a periodic trajectory (libration) of the classical system with the inverted potential and not the action on the doubly asymptotic trajectory. In this expression, the principal term of the pre-exponential factor takes a more elegant form. In the derivation, we merely transform the asymptotic formulas in the mentioned work without going beyond the framework of classical mechanics.
Mots-clés : tunnel effect
Keywords: Schrödinger operator, eigenvalue splitting, quantum double well, libration. 
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A. Yu. Anikin. Librations and ground-state splitting in a multidimensional double-well problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 2, pp. 193-205. http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a4/

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