Hagedorn, George A. 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 \(\varepsilon\to0\). Cited in 2 Documents 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 Keywords:multiple scales; bound states of quantum mechanical systems; particles of large mass; particles of small mass; asymptotic expansions Citations:Zbl 0707.00014 PDFBibTeX XMLCite \textit{G. A. Hagedorn}, in: Nonanticipating operator-differential equations in the class of Bochner measurable functions and existence of optimal controls. . 402--406 (1989; Zbl 0751.47033)