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Multiple scales and the time-independent Born-Oppenheimer approximation. (English) Zbl 0751.47033

Differential equations and applications, Proc. Int. Conf., Columbus/OH (USA) 1988, Vol. I, 402-406 (1989).
Summary: [For the entire collection see Zbl 0707.00014.]
We use the method of multiple scales to study the bound states of quantum mechanical systems which consist of some particles of large mass and some particles of small mass. We show that if the potentials are smooth and the large mass are proportional to \(\varepsilon^{-4}\), then certain eigenvalues and eigenvectors of the Hamiltonian have asymptotic expansions to arbitrarily high order in powers of \(\varepsilon\), as \(\varepsilon\to0\).

MSC:

47N50 Applications of operator theory in the physical sciences
47A55 Perturbation theory of linear operators
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81Q15 Perturbation theories for operators and differential equations in quantum theory

Citations:

Zbl 0707.00014
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