The step-harmonic potential

Luca Rizzi 1, 2 Oliver Piattella 3 Sergio Cacciatori 3 Vittorio Gorini 3
2 GECO - Geometric Control Design
CNRS - Centre National de la Recherche Scientifique : UMR7641, X - École polytechnique, Inria Saclay - Ile de France
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 Piattella, Sergio Cacciatori, Vittorio Gorini. The step-harmonic potential. American Journal of Physics, American Association of Physics Teachers, 2010, pp.19. ⟨10.1119/1.3379290⟩. ⟨hal-01122823⟩

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