## 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

### Keywords:

Schrödinger operator; spectrum; Laplace-Beltrami operator
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