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Author Prager, S. ♦ Hirschfelder, J. O.
Sponsorship USDOE
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword PHYSICS ♦ ATOMS ♦ DIELECTRICS ♦ DIFFERENTIAL EQUATIONS ♦ ELECTRIC CHARGES ♦ ELECTRIC POTENTIAL ♦ ELECTROSTATICS ♦ ENERGY LEVELS ♦ EQUATIONS ♦ HYDROGEN ♦ MATHEMATICS ♦ PERTURBATION THEORY ♦ POISSON EQUATIONS ♦ POLARIZATION ♦ WAVE MECHANICS
Abstract The first-order perturbation equation, using the Dalgarno-Lewis formulation, is arranged in a form analogous to the Poisson equation for the electrostatic potential produced by a charge distribution in a medium of variable dielectric constant. Thus, the Thomson and Dirichlet variational principles of electrostatics can be used to obtain approximate solutions to the first-order penturbation equition for systems in either the ground state or the lowest energy state of a given symmetry. The Thomsom principle provides a useful lower bound to the second-order pertubation energy. The Dirichlet principle is derivable from the Rayleigh-Ritz or Hylleraas principles and gives an upper bound to the second-order energy. For excited states, the Sinanoglu principle provides the upper bound. By optimizing the scaling of the trial penturbed wavefunction, the Hylleraas principle is presented in a somewhat improved form. As an example, the polarizability of atomic hydrogen is used to illustrate both the Thomson and Dirichlet principles and to place upper and lower bounds on the polarizability. (auth)
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 1963-12-15
Publisher Department Univ. of Minnesota, Minneapolis
Journal Journal of Chemical Physics
Volume Number 39
Organization Univ. of Minnesota, Minneapolis


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