Tight lower bounds to eigenvalues of the Schrödinger equation
- 1 August 1980
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 21 (8) , 2182-2192
- https://doi.org/10.1063/1.524700
Abstract
A new tight lower bound to eigenvalues of the Schrödinger equation, which tends to be better than the well‐known Temple lower bound, is presented. The new bound works (as does the Temple bound) for both ground and excited states. Optimization of both the Temple bound and the new tight bound with respect to a variational trial function is discussed. Numerical results are given for the anharmonic oscillator.Keywords
This publication has 20 references indexed in Scilit:
- Two-well oscillatorPhysical Review D, 1978
- Anharmonic oscillator and the analytic theory of continued fractionsPhysical Review D, 1978
- Proof that theIon Has Only One Bound StatePhysical Review Letters, 1977
- Lower Bounds for Eigenvalues with Displacement of Essential SpectraSIAM Journal on Mathematical Analysis, 1972
- Intermediate Hamiltonians for the lithium atomInternational Journal of Quantum Chemistry, 1972
- Improvement of bounds to eigenvalues of operators of form T*TJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1964
- Lower Bounds for Eigenvalues of Schrödinger's EquationPhysical Review B, 1961
- Truncations in the method of intermediate problems for lower bounds to eigenvaluesJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1961
- Lower Bounds for Eigenvalues with Application to the Helium AtomPhysical Review B, 1960
- 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