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

Nicolás Fernández-García ; Oscar Rosas-Ortiz

Symmetry, integrability and geometry: methods and applications, Tome 7 (2011)

Résumé

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.

Détail

Keywords: exactly solvable potentials; scattering process; resonances; Eisenbud–Wigner phase time; dwell time.

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