Singular Bohr-Sommerfeld rules. (English) Zbl 1157.81310

Colin de Verdière, Yves; Parisse, Bernard

Commun. Math. Phys. 205, No. 2, 459-500 (1999).

Summary: The object of this paper is to present a geometrical formulation of the singular Bohr–Sommerfeld rules given in [the authors, Ann. Inst. Henri Poincaré, Phys. Théor. 61, No. 3, 347–367 (1994; Zbl 0845.35076)], in a more general context, including characteristic manifolds with several saddle points. Several examples are detailed and numerical checkings of the results are provided.

MSC:

81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
34E20	Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
47E05	General theory of ordinary differential operators
81R12	Groups and algebras in quantum theory and relations with integrable systems

Citations:

Zbl 0845.35076