Application of an extremum principle to the determination of the diamagnetic susceptibility and form factor of helium

Journal Article · Wed Dec 01 04:00:00 EST 1976 · Phys. Rev., A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.14.1989· OSTI ID:7329991

Shakeshaft, R; Rosenberg, L; Spruch, L

Variational expressions for arbitrary quantum-mechanical matrix elements involve not only trial wave functions but also trial auxiliary Lagrange multipliers, which can be constants, functions, Green's functions, etc. Recently an extremum principle has been proposed as a useful tool for the approximate determination of any Langrange functions that appear; it is the first such tool of general applicability. This extremum principle has here been applied to the variational determination of the diamagnetic susceptibility and form factor of helium; each requires the approximate determination of one Lagrange function. The results, reported on in this paper, demonstrate that the extremum principle can in fact be used in the sense that no singularities appear and the functional that determines the trial Lagrange function L/sub t/ converges monotonically. The results indicate that provided L/sub t/ is roughly as accurate as the trial wave function, the variational estimate of a matrix element can be a significant improvement over the first-order estimate. The present method provides an alternative to the direct approach in which the trial bound-state wave functions are obtained in the course of a Rayleigh-Ritz calculation of the energy. Further studies are needed to determine the relative advantages of the two approaches. (AIP)

• Research Organization: Physics Department, New York University, New York, New York 10003
• OSTI ID: 7329991
• Journal Information: Phys. Rev., A; (United States), Journal Name: Phys. Rev., A; (United States) Vol. 14:6; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
CRYOGENIC FLUIDS
DIFFERENTIAL EQUATIONS
ELEMENTS
EQUATIONS
FLUIDS
FORM FACTORS
FUNCTIONS
HELIUM
LAGRANGE EQUATIONS
MAGNETIC PROPERTIES
MAGNETIC SUSCEPTIBILITY
NONMETALS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
RARE GASES
VARIATIONAL METHODS
WAVE FUNCTIONS