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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 044, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.044
(Mi sigma602)
 

This article is cited in 10 scientific papers (total in 10 papers)

Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time

Nicolás Fernández-Garcíaa, Oscar Rosas-Ortizb

a Instituto de Física, UNAM, AP 20-353, 01000 México D.F., Mexico
b Physics Department, Cinvestav, A.P. 14-740, México DF 07000, Mexico
References:
Abstract: We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases in which the impinging particle is ‘captured’ by the semi-harmonic rectangular potentials. The ‘time of capture’ is connected with the dwell time of the scattered wave. Using the particle absorption method, it is shown that the dwell time $\tau^a_D$ coincides with the phase time $\tau_W$ of Eisenbud and Wigner, calculated as the energy derivative of the reflected wave phase shift. Analytical expressions are derived for the phase time $\tau_W$ of the semi-harmonic delta well and barrier potentials.
Keywords: exactly solvable potentials; scattering process; resonances; Eisenbud–Wigner phase time; dwell time.
Received: December 1, 2010; in final form April 29, 2011; Published online May 5, 2011
Bibliographic databases:
Document Type: Article
Language: English
Citation: Nicolás Fernández-García, Oscar Rosas-Ortiz, “Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time”, SIGMA, 7 (2011), 044, 17 pp.
Citation in format AMSBIB
\Bibitem{FerRos11}
\by Nicol\'as Fern\'andez-Garc{\'\i}a, Oscar Rosas-Ortiz
\paper Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
\jour SIGMA
\yr 2011
\vol 7
\papernumber 044
\totalpages 17
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\crossref{https://doi.org/10.3842/SIGMA.2011.044}
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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