Application of an extremum principle to the variational determination of the generalized oscillator strengths of helium

Authors

J. M. Wadehra, New York UniversityFollow
Larry Spruch, New York University
Robin Shakeshaft, Texas A&M University

Document Type

Article

Abstract

Variational principles have been used extensively for estimating some given functional F(φ, φ^†) where the functions φ and φ^† are well defined by a set of differential equations and boundary conditions but cannot be determined exactly. The variational principle for the estimation of a matrix element of an arbitrary Hermitian operator W involves not only the trial wave functions φ_t but also trial auxiliary Lagrange functions L_t; the L_t depend on the φ_t and on W. To determine the parameters in the L_t efficiently, a functional M(L_tt) is constructed which is an extremum for L_tt=L_t. The technique was recently used successfully in the variational estimation of two diagonal matrix elements. We here use this technique for the variational estimation of an off-diagonal matrix element, the generalized oscillator strengths of helium for the transition between the ground state and the excited 2¹P state. Two L_t's must be determined. Our results on helium indicate that variational estimates are a significant improvement over the first-order estimates. The results are also compared with those obtained nonvariationally using more elaborate ground-and excited-state wave functions; the comparison represents a check on the method. It is not yet clear which of the two approaches is more efficient.

Disciplines

Physics

Recommended Citation

Wadehra JM, Spruch L, & Shakeshaft R. Application of an extremum principle to the variational determination of the generalized oscillator strengths of helium. Phys. Rev. A. 1978;18(2):344-49. doi: 10.1103/PhysRevA.18.344