The European Physical Journal H

, Volume 38, Issue 4, pp 519–534 | Cite as

On lower bounds for polarisability

  • H.E. MontgomeryJr.Email author
  • V.I. Pupyshev


The response of molecular systems to external fields was one of the first areas studied after development of the new quantum mechanics. Early work by Kirkwood and Buckingham developed polarisability lower bounds that are still used today. This work uses an inequality proposed by Linderberg to develop a treatment of polarisability lower bounds that unifies the work of Kirkwood and Buckingham with Hylleraas’ variational perturbation theory. In particular, the prehistory of the works of Kirkwood and Buckingham is described. Numerical examples are presented to demonstrate the convergence of approximate wavefunctions in the confined atom problem. The applicability of dimensional scaling and its utility in the analysis of confined systems are also discussed.


Wave Function Helium Atom Dipole Polarisabilities Ground State Wave Function Diamagnetic Susceptibility 
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© EDP Sciences and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Chemistry Program, Centre College DanvilleDanvilleUSA
  2. 2.Laboratory of Molecular Structure and Quantum Mechanics, Department of Chemistry, Lomonosov Moscow State University MoscowMoscowRussia

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