Abstract
In physics and chemistry the Born-Oppenheimer approximation is a very important method for analyzing the spectrum of molecules1). It is based on the important fact that the molecular Schrödinger operator contains one small parameter, the ratio k4 of the electronic to the nuclear mass2). Perturbation theory in this parameter is however very singular.
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References
Aguilar J. and Combes J.M., 1971; A class of Analytic Perturbations for One-body Schrödinger Hamiltonians, Com.Math.Phys. 22, 269–279.
Born M. and Oppenheimer R., 1927; Zur Quantentheorie der Molekeln, Annalen der Physik 84, 457.
Brattsev V.F., 1965; Dokl.Akad.Nauk. SSSR 16o, 570.
Brezin E. and Zinn-Justin J., 1979; Expansion of the \(H_2^ + \) ground state energy in inverse powers of the distance between the two protons; Le journal de physique, lettres, 40L-511.
Combes J.M. and Seiler R., 1978; Regularity and Asymptotic Properties of the Discrete Spectrum of Electronic Hamiltonians; Int.J. of Quantum Chemistry 14, 213.
Combes J.M. and Seiler R., 1980; Spectral Properties of Atomic and Molecular Systems, Ed.G.Wooley, Plenum.
Combes J.M., Duclos P. and Seiler R.,1981; Decoupling and Krein’s Formula I, to appear.
Combes J.M. and Thomas L., 1973; Asymptotic Behaviour of Eigenfunctions for Multiparticle Schrödinger Operators; Commun.math.Phys. 34, 251.
Deift P., Hunziker W., Simon B., Vock E.,1979; Pointwise Bounds of Eigenfunctions and Wave Packets in N-Body Quantum Systems IV; Com. Math. Phys. 64, 1–34.
Dieudonné J., 1968; Calcul Infinitesimal, Chapter VIII. 7, Herman, Paris.
Duclos P., Thèse, Dept.de Mathématique Université de Toulon.
Epstein S., 1966; Ground-State Energy of a Molecule in the Adiabatic Approximation, J.Chem.44, 863 and 44, 4062.
Herring C., 1962; Critique of the Heitler-Landau method of calculating spin coupling at large distances, Rev.Mod.Phys. 34, 631–645.
Hoffmann-Osterhoff T., 1980; A Compairison Theorem for Differential Inequalities with Applications in Quantum Mechanics; Journal of Physics AB, 417.
Hoffmann-Osterhoff M. and Seiler R., 1981; to appear in Phys. Rev.A.
Kato T., 1966; Perturbation theory for linear Operators, Springer-Verlag, Berlin.
Kato T., 1957; Commun.Pure and Appl.Math. X, 151.
Komarov J.N., Ponomarev L.I., Slavianov S.I., 1976; Spherical and Coulomb Spheroidal functions. Nauka, Moscow (in Russian).
Krein M., 1946; Über Resolventen hermitescher Operatoren mit Defektindex (m,m) Doklady Akad.Nauk. SSSR 52 No. 8, 657–660.
Lieb E. and Simon B., 1978; Monotonicity of the Electronic Contribution to the Born-Oppenheimer Energy, J.Phys.B. 5 37.
Morgan J.D. Ill and Simon B., 1980; Behavior of Molecular Potential Energy Curves for Large Nuclear Seperations; Int.J.Quant. Chemistry, 17, 1143.
Pack R.T. and Hirschfelder J.O., 1968; Separation of Rotational Coordinates from the N-electrons Diatomic Schrödinger Equation, Journal of Chemical Physics 49, 4009–4020.
Protter M.H. and Weinberger H.F.,1967; Maximum Principles in Differential Equations, Prentice-Hall, Juc.
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© 1981 Plenum Press, New York
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Combes, J.M., Duclos, P., Seiler, R. (1981). The Born-Oppenheimer Approximation. In: Velo, G., Wightman, A.S. (eds) Rigorous Atomic and Molecular Physics. NATO Advanced Study Institutes Series, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3350-0_5
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