SEMICLASSICAL APPROXIMATION FOR SCHRODINGER-OPERATORS ON A 2-SPHERE AT HIGH-ENERGY

Let H=-Delta(S)+V be a Schrodinger operator acting in L(2)(S), with S the two-dimensional unit sphere, Delta(S) the spherical Laplacian, and V a smooth potential. Approximate eigenfunctions and eigenvalues for H are obtained involving expansions in inverse powers of the classical angular momentum variables, provided that these variables are in a re gion of phase space where the corresponding classical Hamiltonian is n early integrable. The analysis is carried out in a Bargmann representa tion, where Delta(S) becomes a quadratic expression in the sum of two quantum harmonic oscillator Hamiltonians, and V becomes a pseudodiffer ential operator. (C) 1995 American Institute of Physics.