Analytical Shannon information entropies for all discrete multidimensional hydrogenic states
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty measure to quantify the electronic spreading and to mathema...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/40221 |
| Acceso en línea: | https://hdl.handle.net/10115/40221 |
| Access Level: | acceso embargado |
| Palabra clave: | Dimensional dependence of Shannon entropy Entropic uncertainty Shannon entropy of multidimensional hydrogenic states |
| Sumario: | The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty measure to quantify the electronic spreading and to mathematically formalize the Heisenberg uncertainty principle, partially because it does not depend on any specific point of their multidimensional domain of definition. In this work, the radial and angular parts of the Shannon entropies for all the discrete stationary states of the multidimensional hydrogenic systems are obtained from first principles; that is, they are given in terms of the states' principal and magnetic hyperquantum numbers (n, μ1, μ2, …, μD−1), the system's dimensionality D and the nuclear charge Z in an analytical, compact form. Explicit expressions for the total Shannon entropies are given for the quasi-spherical states, which conform to a relevant class of specific states of the D-dimensional hydrogenic system characterized by the hyperquantum numbers μ1 = μ2 … = μD−1 = n − 1, including the ground state. |
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