Lower bounds for quartic anharmonic and double-well potentials
- 1 January 1993
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 34 (1) , 1-11
- https://doi.org/10.1063/1.530375
Abstract
Rigorous and remarkably accurate lower bounds to the lower eigenvalue spectrum of the Schrödinger equation with quartic anharmonic and symmetric double-well potentials of the form V(A,B)=Ax2/2+Bx4(B≥0) are presented. This procedure exploits some exactly soluble model potentials and appears to be of quite general utility.Keywords
This publication has 11 references indexed in Scilit:
- Some observations on the nature of solutions for the interaction V(x)=x2+(λx2/(1+gx2))Journal of Physics A: General Physics, 1990
- Exact solutions of the Schrödinger equation for nonseparable anharmonic oscillator potentials in two dimensionsJournal of Mathematical Physics, 1989
- Pairs of analytical eigenfunctions for the x2+ λ x2/(1 + gx2) interactionJournal of Physics A: General Physics, 1989
- On the simultaneous eigenproblem for the x2- λ x2(1 + gx2)-1interaction: extension of Gallas' resultsJournal of Physics A: General Physics, 1989
- A unified treatment of Schrodinger's equation for anharmonic and double well potentialsJournal of Physics A: General Physics, 1989
- A Rodrigues formula approach to determining closed-form solutions to the Schrödinger equation for symmetric anharmonic oscillatorsJournal of Mathematical Physics, 1989
- Exact analytical eigenfunctions for the x2+ λ x2/(1+gx2) interactionJournal of Physics A: General Physics, 1988
- The Schrodinger equation for the x2+λx2/(1+gx2) interactionJournal of Physics A: General Physics, 1987
- Studies in Perturbation Theory. X. Lower Bounds to Energy Eigenvalues in Perturbation-Theory Ground StatePhysical Review B, 1965
- A Procedure for Estimating EigenvaluesJournal of Mathematical Physics, 1962