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Multiple wells in the semi-classical limit. III: Interaction through non- resonant wells. (English) Zbl 0597.35023
Cet article est le 3ème d’une série de 6 articles des auteurs concernant l’étude de l’effet tunnel en mécanique semi-classique pour l’équation de Schrödinger: \(P=-h^ 2\Delta +V\) publiés ou à paraître dans les revues suivantes [Commun. Partial Differ. Equations 9, 337-408 (1984; Zbl 0546.35053); II: Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 42, 127-212 (1985; Zbl 0595.35031); IV: (see the following review); V: in Comment topics in partial differential equations (1986) Kinokuniya company LTD. Tokyo; VI: Ann. Inst.Henri Poincaré, Nouv. Sér., Sect. A (to appear)].
On considère dans cet article le cas où certains des puits \((= composantes\) connexes de \(V<E_ 0)\) n’ont pas de spectre dans un intervalle proche de \(E_ 0\) et l’on observe que les effets tunnels entre les puits à spectre (= résonnants) peuvent être beaucoup plus petits.

MSC:
35J10 Schrödinger operator, Schrödinger equation
35P15 Estimates of eigenvalues in context of PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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[1] , Foundations of Mechanics, Benjamin/Cumming, Publ. Company 1978
[2] Helfer, Comm. P.D.E. 9 pp 337– (1984)
[3] Helfer, Ann. Inst. Poincaré
[4] Lascar, Comm. P.D.E.
[5] Menikoff, The nonsemi bounded case, Journal d’Analyse Mathématique 35 pp 123– (1979) · Zbl 0436.35065
[6] Pham, Prépubl. de Math. de l’Univ. de Nice, n 14 (1983)
[7] Simon, Bull. A.M.S. pp 323– (1983)
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