UPPER AND LOWER BOUNDS FOR GROUNDSTATE SECOND-ORDER PERTURBATION ENERGY

Journal Article · Sun Dec 15 04:00:00 EST 1963 · Journal of Chemical Physics (U.S.)

DOI:https://doi.org/10.1063/1.1734192· OSTI ID:4138587

Prager, S; Hirschfelder, J O

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)

• Research Organization: Univ. of Minnesota, Minneapolis
• Sponsoring Organization: USDOE
• NSA Number: NSA-18-007413
• OSTI ID: 4138587
• Journal Information: Journal of Chemical Physics (U.S.), Journal Name: Journal of Chemical Physics (U.S.) Vol. Vol: 39; ISSN JCPSA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ATOMS
DIELECTRICS
DIFFERENTIAL EQUATIONS
ELECTRIC CHARGES
ELECTRIC POTENTIAL
ELECTROSTATICS
ENERGY LEVELS
EQUATIONS
HYDROGEN
MATHEMATICS
PERTURBATION THEORY
PHYSICS
POISSON EQUATIONS
POLARIZATION
WAVE MECHANICS