Upper Bounds for Errors of Expectations in the Few-Body Problem
- 20 October 1967
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 162 (4) , 878-883
- https://doi.org/10.1103/physrev.162.878
Abstract
Exact upper bounds are established for the errors associated with approximate computations of total, kinetic, and potential energies of a few-body system. As a consequence, error bounds are also established for arbitrary coordinate functions. Reduction methods are developed to treat expectations of coordinate functions which are divergent at some spatial point, e.g., the delta function or the inverse square, or at infinity, e.g., the mean-square radius. Positronium is used as a test case to study the relative accuracy of the estimates.Keywords
This publication has 8 references indexed in Scilit:
- Polarized wave functions for a few-body model nucleusNuclear Physics A, 1967
- Error Bounds for Expectation ValuesReviews of Modern Physics, 1963
- Variational calculations on the binding energy of the alpha particle (I): Hard-core potentialsNuclear Physics, 1963
- Limits of Error for the Electron Density, Spin Density, and Atomic Form Factor in Quantum-Mechanical CalculationsPhysical Review B, 1963
- Die Bedeutung des Energievergleiches für die Güte einer NäherungslösungZeitschrift für Naturforschung A, 1961
- Ground State of the Helium Atom. IIPhysical Review B, 1959
- A Lower Limit for the Ground State of the Helium AtomPhysical Review B, 1932
- The theory of Rayleigh's principle as applied to continuous systemsProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1928