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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
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
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.
Linking options:
https://www.mathnet.ru/eng/sigma602 https://www.mathnet.ru/eng/sigma/v7/p44
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