Convergence of resonance expansions in quantum wave buildup
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Sociedad Mexicana de Física A.C.
2016
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| _version_ | 1866817171411173376 |
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| author | Alberto Hernández-Maldonado |
| author_facet | Alberto Hernández-Maldonado |
| contents | Convergence of resonance expansions in quantum wave buildup Alberto Hernández-Maldonado Roberto Romo Jorge Villavicencio Física, Astronomía y Matemáticas Gamow states Resonance expansion The convergence of stationary and dynamical resonance expansions that involve complex eigenenergies of the system is analyzed in thecalculation of the electronic probability density along the internal region of a resonant structure. We show that an appropriate selection of theresonance contributions leads to results that are numerically indistinguishable from the exact Hermitian calculation. In particular, the roleplayed by the anti-resonances in the convergence process is emphasized. An interesting scaling property of the Schr ̈odinger equation, andthe stationary resonance expansion, useful for the analysis of convergence of families of systems, is also demonstrated. The convergence ofa dynamical resonance expansion based on a Moshinsky shutter setup, is explored in the full time domain. In particular, we explore the buildprocess of the electronic probability density in the transient regime, analyzing the contributions of different resonant states in the earlieststages of the buildup process. We also analyze the asymptotic limit of very long times, converging in the latter case to the stationary solutionprovided by the exact Hermitian calculation. 2016 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57045452012 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.3 Vol.62 |
| format | Artículo científico |
| id | redalyc_57045452012 |
| language | en |
| publishDate | 2016 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Convergence of resonance expansions in quantum wave buildup Alberto Hernández-Maldonado Física, Astronomía y Matemáticas Gamow states Resonance expansion Convergence of resonance expansions in quantum wave buildup Alberto Hernández-Maldonado Roberto Romo Jorge Villavicencio Física, Astronomía y Matemáticas Gamow states Resonance expansion The convergence of stationary and dynamical resonance expansions that involve complex eigenenergies of the system is analyzed in thecalculation of the electronic probability density along the internal region of a resonant structure. We show that an appropriate selection of theresonance contributions leads to results that are numerically indistinguishable from the exact Hermitian calculation. In particular, the roleplayed by the anti-resonances in the convergence process is emphasized. An interesting scaling property of the Schr ̈odinger equation, andthe stationary resonance expansion, useful for the analysis of convergence of families of systems, is also demonstrated. The convergence ofa dynamical resonance expansion based on a Moshinsky shutter setup, is explored in the full time domain. In particular, we explore the buildprocess of the electronic probability density in the transient regime, analyzing the contributions of different resonant states in the earlieststages of the buildup process. We also analyze the asymptotic limit of very long times, converging in the latter case to the stationary solutionprovided by the exact Hermitian calculation. 2016 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57045452012 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.3 Vol.62 |
| title | Convergence of resonance expansions in quantum wave buildup |
| topic | Física, Astronomía y Matemáticas Gamow states Resonance expansion |
| url | https://www.redalyc.org/articulo.oa?id=57045452012 |