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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146861 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862683403343626240 |
|---|---|
| author | Fernández-García, N. Rosas-Ortiz, O. |
| author_facet | Fernández-García, N. Rosas-Ortiz, O. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:55:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146861 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:55:56Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fernández-García, N. Rosas-Ortiz, O. 2019-02-11T18:04:59Z 2019-02-11T18:04:59Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/146861 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time Article published earlier |
| spellingShingle | Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time Fernández-García, N. Rosas-Ortiz, O. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146861 |
| work_keys_str_mv | AT fernandezgarcian rectangularpotentialsinasemiharmonicbackgroundspectrumresonancesanddwelltime AT rosasortizo rectangularpotentialsinasemiharmonicbackgroundspectrumresonancesanddwelltime |