Lower bounds to eigenvalues in atomic physics
Modifications to the method of intermediate problems are presented for the improvement of its application to atomic systems. The successful calculations of Freund and Hill for the lower-bounding problem of lithium presented new problems with efficiency, accuracy, solving of large matrices, and rates of convergence. The partitioning technique of P. O. Loewdin is applied to the lower-bounding matrix of Li/sup +/ in order to create smaller matrices. The lower-bounding eigenvalues of the partitioned matrix are found to be within 0.1% of the corresponding nonpartitioned eigenvalues. The difficulty with slow convergence can be examined by choosing a basis set for the lower-bounding calculation, which includes more of the analytic structure of the exact wave function. Calculations for the new matrix elements which arise from this choice of basis set are presented. In particular, recursion relations are given for the matrix elements of 1/r/sub 12//sup 2/.
- Research Organization:
- Delaware Univ., Newark (USA)
- OSTI ID:
- 6400847
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ATOMIC PHYSICS
CALCULATION METHODS
CATIONS
CHARGED PARTICLES
EIGENVALUES
FUNCTIONS
IONS
LITHIUM IONS
MATRICES
MATRIX ELEMENTS
PHYSICS
RECURSION RELATIONS
WAVE FUNCTIONS