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

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

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 t...

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Datum:2011
Hauptverfasser: Fernández-García, N., Rosas-Ortiz, O.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2011
Schriftenreihe:Symmetry, Integrability and Geometry: Methods and Applications
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/146861
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

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spelling irk-123456789-1468612019-02-12T01:24:36Z Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time Fernández-García, N. Rosas-Ortiz, O. 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. 2011 Article 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. 1815-0659 2010 Mathematics Subject Classification: 35Q40; 35B34; 81U30; 81Q60 DOI:10.3842/SIGMA.2011.044 http://dspace.nbuv.gov.ua/handle/123456789/146861 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Fernández-García, N.
Rosas-Ortiz, O.
spellingShingle Fernández-García, N.
Rosas-Ortiz, O.
Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Fernández-García, N.
Rosas-Ortiz, O.
author_sort Fernández-García, N.
title Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
title_short Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
title_full Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
title_fullStr Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
title_full_unstemmed Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
title_sort rectangular potentials in a semi-harmonic background: spectrum, resonances and dwell time
publisher Інститут математики НАН України
publishDate 2011
url http://dspace.nbuv.gov.ua/handle/123456789/146861
citation_txt 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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT fernandezgarcian rectangularpotentialsinasemiharmonicbackgroundspectrumresonancesanddwelltime
AT rosasortizo rectangularpotentialsinasemiharmonicbackgroundspectrumresonancesanddwelltime
first_indexed 2025-07-11T00:47:46Z
last_indexed 2025-07-11T00:47:46Z
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