A solvable double well
Abstract
We study the quantum behaviour of a particle moving in a one-dimensional double well potential. This double well is obtained by gluing together, at the origin, two shifted harmonic oscillator potentials. The Schr\"odinger equation is exactly solvable. The requirement that discontinuities, in the wavefunction and its first derivative, are absent at the origin, leads to the quantisation of the energy eigenvalues. We also show that oscillations in time take place between two nearby single harmonic oscillator ground states. Finally, the double well potential is augmented by a Dirac delta-function potentials at the origin and the corresponding Schr\"odinger equation is solved.
Cite
@article{arxiv.1606.06637,
title = {A solvable double well},
author = {N. Mohammedi and Tim. R. Morris},
journal= {arXiv preprint arXiv:1606.06637},
year = {2017}
}
Comments
This paper is withdrawn because the model is already treated in a substantially similar way in Merzbacher's text-book