Perturbative technique as an alternative to the WKB method applied to the double-well potential
- 1 October 1982
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 23 (10) , 1835-1845
- https://doi.org/10.1063/1.525236
Abstract
We give an explicit and complete perturbation theoretical analysis of the solutions and the eigenvalues of the Schrödinger equation for the double-well potential. In particular we demonstrate the matching of various branches of the solutions over the entire range of the independent variable, and we calculate the splitting of eigenvalues due to the finite height of the central hump of the potential.Keywords
This publication has 32 references indexed in Scilit:
- The band-structure of a one-dimensional, periodic system in a scaling limitAnnals of Physics, 1979
- No horn of singularities for the double well anharmonic oscillatorPhysics Letters B, 1978
- Singular perturbations and asymptotic eigenvalue degeneracyCommunications on Pure and Applied Mathematics, 1976
- Large coupling expansions for eigenenergies and Regge trajectories of the Yukawa potentialJournal of Mathematical Physics, 1973
- Normalization of Certain Higher-Order Phase-Integral Approximations for Wavefunctions of Bound States in a Potential Well. IIJournal of Mathematical Physics, 1972
- On One-Dimensional Model for Exchange ForcesThe Journal of Chemical Physics, 1971
- Perturbation Theory for Large Coupling Constants Applied to the Gauss PotentialJournal of Mathematical Physics, 1970
- Pade approximants and the anharmonic oscillatorPhysics Letters B, 1969
- High-Energy Scattering for Yukawa PotentialsJournal of Mathematical Physics, 1968
- Oscillators Perturbed by Gaussian BarriersThe Journal of Chemical Physics, 1963