Abstract
We consider the Schrödinger operatorP(h) for a polyatomic molecule in the semiclassical limit where the mass ratioh 2 of electronic to nuclear mass tends to zero. We obtain WKB-type expansions of eigenvalues and eigenfunctions ofP(h) to all orders inh. 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 ofh-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.
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Communicated by T. Spencer
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Klein, M., Martinez, A., Seiler, R. et al. On the Born-Oppenheimer expansion for polyatomic molecules. Commun.Math. Phys. 143, 607–639 (1992). https://doi.org/10.1007/BF02099269
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DOI: https://doi.org/10.1007/BF02099269