On the relative accuracies of eigenvalue bounds
- 1 September 1973
- journal article
- Published by IOP Publishing in Journal of Physics B: Atomic and Molecular Physics
- Vol. 6 (9), 1741-1750
- https://doi.org/10.1088/0022-3700/6/9/017
Abstract
The authors examine the relative accuracies of the Rayleigh upper bound and the Temple (1928), Weinstein (1934) and Stevenson (1938) lower bounds in the limit of an accurate trial function. This analysis leads to an understanding of why lower bounds have usually been observed to have larger errors than upper bounds using the same trial function. In the second part a simple relationship is given between the errors in classical lower bounds, and intermediate- operator lower bounds. The relative errors of Rayleigh and intermediate-operator methods are examined in the limit of an accurate trial function.Keywords
This publication has 15 references indexed in Scilit:
- On the Temple lower bound for eigenvaluesJournal of Physics A: General Physics, 1972
- Improved Equation for Lower Bounds to Eigenvalues; Bounds for the Second-Order Perturbation EnergyThe Journal of Chemical Physics, 1969
- A Lower Bound Procedure for Energy EigenvaluesPhysical Review B, 1964
- ,, andStates ofand of HePhysical Review B, 1962
- A Procedure for Estimating EigenvaluesJournal of Mathematical Physics, 1962
- Lower Bounds for Eigenvalues of Schrödinger's EquationPhysical Review B, 1961
- Lower-bound energies and the Virial theorem in wave mechanicsMathematical Proceedings of the Cambridge Philosophical Society, 1961
- Lower Bounds for Eigenvalues with Application to the Helium AtomPhysical Review B, 1960
- LOWER BOUNDS FOR EIGENVALUES WITH APPLICATION TO THE HELIUM ATOMProceedings of the National Academy of Sciences, 1959
- On the Upper and Lower Bounds of EigenvaluesJournal of the Physics Society Japan, 1949