Dynamics of the probability density in the internal region of a double for a Dirac delta potential
Based on exact analytical solutions of the time-dependent Schrödinger equation, and initial conditions of plane waves cut in x-space by an absorbing or reflecting quantum shutter, the dynamic behavior of the electronic probability density or buildup is analyzed, in the internal region of a double Di...
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Universidad Autónoma de Baja California
2020
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recit-article-622022-10-25T23:34:58Z Dynamics of the probability density in the internal region of a double for a Dirac delta potential Dinámica de la densidad de probabilidad en la región interna de un potencial doble delta de Dirac Hernández Maldonado, Alberto Quantum transients Double delta potential Moshinsky shutter. Transitorios cuánticos Potencial doble delta Obturador de Moshinsky. Based on exact analytical solutions of the time-dependent Schrödinger equation, and initial conditions of plane waves cut in x-space by an absorbing or reflecting quantum shutter, the dynamic behavior of the electronic probability density or buildup is analyzed, in the internal region of a double Dirac delta potential double, from very short times (given in half-lives), until reaching the stationary situation. The buildup is compared between both cases, absorbent and reflective quantum shutter, finding that for short times the buildup depends on the initial condition (IC) used, while for long times, it is independent of said IC. Using the reflecting IC, the buildup is analyzed from practically zero time, until the steady-state is reached. The results found may be relevant in the context of rapid response in devices known as resonant tunneling diodes. Con base en soluciones analíticas exactas de la ecuación de Schrödinger dependiente del tiempo, y condiciones iniciales de ondas planas cortadas en el espacio x mediante un obturador cuántico absorbente o reflejante, se analiza el comportamiento dinámico de la densidad de probabilidad electrónica o buildup, en la región interna de un potencial doble delta de Dirac, desde tiempos (dados en vidas medias) muy pequeños, hasta alcanzar la situación estacionaria. Se compara el buildup entre ambos casos, absorbente y reflejante, encontrando que para tiempos cortos el buildup depende de la condición inicial (CI) utilizada, mientras que, para tiempos grandes, es independiente de dicha CI. Usando la CI reflejante, se analiza el buildup desde un tiempo prácticamente cero, hasta que se alcanza la situación estacionaria. Los resultados encontrados pueden ser relevantes en el contexto de la respuesta rápida en los dispositivos conocidos como diodos de tunelaje resonante. Universidad Autónoma de Baja California 2020-09-30 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Research article Artículo de investigación application/pdf text/html application/xml https://recit.uabc.mx/index.php/revista/article/view/62 10.37636/recit.v33173180 REVISTA DE CIENCIAS TECNOLÓGICAS; Vol. 3 No. 3 (2020): July-September; 173-180 REVISTA DE CIENCIAS TECNOLÓGICAS; Vol. 3 Núm. 3 (2020): Julio-Septiembre; 173-180 2594-1925 spa https://recit.uabc.mx/index.php/revista/article/view/62/121 https://recit.uabc.mx/index.php/revista/article/view/62/122 https://recit.uabc.mx/index.php/revista/article/view/62/176 Copyright (c) 2020 Alberto Hernández Maldonado http://creativecommons.org/licenses/by/4.0 |
| institution |
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| collection |
OJS |
| language |
spa |
| format |
Online |
| author |
Hernández Maldonado, Alberto |
| spellingShingle |
Hernández Maldonado, Alberto Dynamics of the probability density in the internal region of a double for a Dirac delta potential |
| author_facet |
Hernández Maldonado, Alberto |
| author_sort |
Hernández Maldonado, Alberto |
| title |
Dynamics of the probability density in the internal region of a double for a Dirac delta potential |
| title_short |
Dynamics of the probability density in the internal region of a double for a Dirac delta potential |
| title_full |
Dynamics of the probability density in the internal region of a double for a Dirac delta potential |
| title_fullStr |
Dynamics of the probability density in the internal region of a double for a Dirac delta potential |
| title_full_unstemmed |
Dynamics of the probability density in the internal region of a double for a Dirac delta potential |
| title_sort |
dynamics of the probability density in the internal region of a double for a dirac delta potential |
| description |
Based on exact analytical solutions of the time-dependent Schrödinger equation, and initial conditions of plane waves cut in x-space by an absorbing or reflecting quantum shutter, the dynamic behavior of the electronic probability density or buildup is analyzed, in the internal region of a double Dirac delta potential double, from very short times (given in half-lives), until reaching the stationary situation. The buildup is compared between both cases, absorbent and reflective quantum shutter, finding that for short times the buildup depends on the initial condition (IC) used, while for long times, it is independent of said IC. Using the reflecting IC, the buildup is analyzed from practically zero time, until the steady-state is reached. The results found may be relevant in the context of rapid response in devices known as resonant tunneling diodes. |
| publisher |
Universidad Autónoma de Baja California |
| publishDate |
2020 |
| url |
https://recit.uabc.mx/index.php/revista/article/view/62 |
| _version_ |
1792095368571256832 |
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