Puits multiples en mécanique semi-classique. V: Étude des minipuits. (Multiple wells in semi-classical mechanics. V: Study of miniwells). (French) Zbl 0628.35024

Helffer, B.; Sjöstrand, J.

Current topics in partial differential equations, Pap. dedic. S. Mizohata Occas. 60th Birthday, 133-186 (1986).

[For the entire collection see Zbl 0604.00006.]
This is the fifth paper in a series of six papers dealing with the tunnel effect in semiclassical mechanics. [For part IV see Commun. Partial Differ. Equations 10, 245-340 (1985; Zbl 0597.35024).] In this particular paper the operator \(P=-h^ 2\Delta +V_ 0+hV_ 2\) is examined on a compact Riemannian manifold M (or \(M={\mathbb{R}}^ n)\). Since the results require a lot of notation and some knowledge of the preceding papers we refer to the paper’s introduction for detailed information.

Reviewer: N.Jacob

MSC:

35J10	Schrödinger operator, Schrödinger equation
58J50	Spectral problems; spectral geometry; scattering theory on manifolds
35P25	Scattering theory for PDEs

Keywords:

multiple well; W.K.B.-approximation; Schrödinger-operator; tunnel effect; semiclassical mechanics; compact Riemannian manifold

Citations:

Zbl 0604.00006; Zbl 0597.35024