The Step-Harmonic Potential
Quantum Physics
2010-07-16 v2 Mathematical Physics
math.MP
General Physics
Abstract
We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit.
Cite
@article{arxiv.0912.3198,
title = {The Step-Harmonic Potential},
author = {Luca Rizzi and Oliver F. Piattella and Sergio L. Cacciatori and Vittorio Gorini},
journal= {arXiv preprint arXiv:0912.3198},
year = {2010}
}
Comments
19 pages, 7 figures