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Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
Інший ID:
2010 Mathematics Subject Classification: 35Q40; 35B34; 81U30; 81Q60
DOI:10.3842/SIGMA.2011.044
DOI:10.3842/SIGMA.2011.044
Посилання:
Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time / N. Fernández-García, O. Rosas-Ortiz // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 56 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
The support of CONACyT and DGAPA (UNAM) is acknowledged.
Дата:
2011
Переглядів:
516
Завантажень:
178
Анотація:
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.
