ON THE BORN-OPPENHEIMER EXPANSION FOR POLYATOMIC-MOLECULES

We consider the Schrodinger operator P(h) for a polyatomic molecule in the semiclassical limit where the mass ratio h2 of electronic to nuclear mass tends to zero. We obtain WKB-type expansions of eigenvalues and eigenfunctions of P(h) to all orders in h. This allows to treat the splitting of the ground state energy of a non-planar molecule. Our class of potentials covers the physical case of the Coulomb interaction. We use methods of h-pseudodifferential operators with operator valued symbols, which by use of appropriate coordinate changes in local coordinate patches covering the classically accessible region become applicable even to our class of singular potentials.Physics, MathematicalSCI(E)74ARTICLE3607-63914