Upper and lower bounds to eigenvalues from variational functionals
- 1 June 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 35 (11) , 4861-4863
- https://doi.org/10.1103/physreva.35.4861
Abstract
Upper and lower bounds to the energy of quantum-mechanical parameter-dependent systems are obtained from variational functionals. Results are shown for the Zeeman effect in hydrogen and the anharmonic oscillator.Keywords
This publication has 17 references indexed in Scilit:
- Rigorous analytical lower bound on the ground-state energies of hydrogenic atoms in high magnetic fieldsPhysical Review A, 1986
- A method for summing strongly divergent perturbation series: The Zeeman effect in hydrogenPhysica A: Statistical Mechanics and its Applications, 1984
- A new variational approach to the hydrogen atom in magnetic fieldsThe European Physical Journal A, 1984
- Geometric approach to the semiclassical bound-state energies of quantum-mechanical modelsThe Journal of Chemical Physics, 1984
- Calculation of bound‐state energies from a variational functional methodInternational Journal of Quantum Chemistry, 1984
- Eigenvalues of anharmonic oscillators from a variational functional methodJournal of Mathematical Physics, 1984
- Analytical expressions for the eigenvalues of anharmonic oscillatorsPhysica A: Statistical Mechanics and its Applications, 1983
- Comments about energies of parameter-dependent systemsPhysical Review A, 1983
- Solutional method for the energies of a parameter-dependent systemPhysical Review A, 1979
- Energies of Parameter-Dependent SystemsPhysical Review Letters, 1979