Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 044, 17 pages      arXiv:1104.5695      https://doi.org/10.3842/SIGMA.2011.044
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

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

Nicolás Fernández-García a and Oscar Rosas-Ortiz b
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

Received December 01, 2010, in final form April 29, 2011; Published online May 05, 2011

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 τDa coincides with the phase time τW of Eisenbud and Wigner, calculated as the energy derivative of the reflected wave phase shift. Analytical expressions are derived for the phase time τW of the semi-harmonic delta well and barrier potentials.

Key words: exactly solvable potentials; scattering process; resonances; Eisenbud-Wigner phase time; dwell time.

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