Singular Bohr-Sommerfeld Rules for 2D Integrable Systems

Details Singular Bohr-Sommerfeld Rules for 2D Integrable Systems Singular Bohr-Sommerfeld Rules for 2D Integrable Systems

2000-05-26

arxiv.org/abs/math/0005264v1

Mathematics

Analysis of PDEs

postscript, 61 pages, figures best seen in color. Preprint Institut Fourier

Scientific paper

In this paper, we describe Bohr-Sommerfeld rules for semi-classical completely integrable systems with 2 degrees of freedom with non degenerate singularities (Morse-Bott singularities) under the assumption that the energy level of the first Hamiltonian is non singular. The more singular case of {\it focus-focus} singularities is studied in [Vu Ngoc San, CPAM 2000] and [Vu Ngoc San, PhD 1998] The case of 1 degree of freedom has been studied in [Colin de Verdiere-Parisse, CMP 1999] Our theory is applied to some famous examples: the geodesics of the ellipsoid, the $1:2$-resonance, and Schroedinger operators on the sphere $S^2$. A numerical test shows that the semiclassical Bohr-Sommerfeld rules match very accurately the ``purely quantum'' computations.

Affiliated with

Also associated with

No associations

Rating

Singular Bohr-Sommerfeld Rules for 2D Integrable Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singular Bohr-Sommerfeld Rules for 2D Integrable Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular Bohr-Sommerfeld Rules for 2D Integrable Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-707146