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Effet tunnel pour l’opérateur de Schrödinger semi-classique. I. (Tunnel effect for the semiclassical Schrödinger operator). (French) Zbl 0607.35026
Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1985, No. 2, 38 p. (1985).
The authors give results on their quasiclassical treatment of Schrödinger operators. Among other things a quasiclassical model for mulecules and Witten’s treatment of the Morse’s inequalities are given. Moreover estimates on the exponential decay of eigenfunctions are obtained. Further results and details of the proofs are found in ”Resonances en limite semi-classique” [Bull. Soc. Math. Fr., Memoire (nouvelle serie) 24/25, Suppl. Bull. Soc. Math. Fr. 114, Fascicule 3 (1986)].
Reviewer: H.Siedentop

MSC:
35J10 Schrödinger operator, Schrödinger equation
35S05 Pseudodifferential operators as generalizations of partial differential operators
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