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On the Born-Oppenheimer expansion for polyatomic molecules. (English) Zbl 0754.35099

The Schrödinger operator \(P(h)\) for a polyatomic molecule with Coulomb interactions is discussed in the limit where the mass ratio \(h^ 2\) of electronic to nuclear mass tends to zero. Asymptotic expansions of eigenvalues and eigenfunctions of \(P(h)\) are obtained to all orders in \(h\). This justifies the Born-Oppenheimer expansion: M. Born and R. Oppenheimer [Annal. Phys. 84, 457 ff. (1927)] in the physically relevant case.
Reviewer: J.Asch (Berlin)

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
81V55 Molecular physics
35J10 Schrödinger operator, Schrödinger equation
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