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Analyse semi-classique de l’opérateur de Schrödinger sur la sphère. (Semi-classical analysis of the Schrödinger operator on the sphere). (French) Zbl 0745.58046

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1990-1991, No.XXIV, 9 p. (1991).
The article is a survey of results on the spectrum of the Schrödinger operator on the sphere \(S^ 2\), i.e. \(-\Delta+V(x)\) where \(-\Delta\) is the Laplace-Beltrami operator and \(V(x)\) a smooth potential. Results of various authors are cited without proofs.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds
35J10 Schrödinger operator, Schrödinger equation
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