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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.

Keywords

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

R2 v1 2026-06-21T14:24:43.616Z