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

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 ${\tau }_D^a$ 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.

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Cited by in corpus (4)

• Resonances and antibound states of Pöschl-Teller potential: Ladder operators and SUSY partners
• The rigged Hilbert space approach to the Gamow states
• Leaky modes of waveguides as a classical optics analogy of quantum resonances
• Negative time delay for wave reflection from a one-dimensional semi-harmonic well