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arXiv · 0912.3198

The Step-Harmonic Potential

Luca Rizzi·Oliver F. Piattella·Sergio L. Cacciatori·Vittorio Gorini
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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.

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Luca Rizzi, Oliver F. Piattella, Sergio L. Cacciatori, Vittorio Gorini. 2009-12-16. The Step-Harmonic Potential. https://doi.org/10.1119/1.3379290

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