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arXiv · 1509.08900

Fisher's information for the position-dependent mass Schrödinger system

B. J. Falaye·F. A. Serrano·Shi-Hai Dong
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Abstract

This study presents the Fisher information for the position-dependent mass Schrödinger equation with hyperbolical potential {$V(x)=-V_0{\rm csch}^2(ax)$}. The analysis of the quantum-mechanical probability for the ground and exited states $(n=0, 1, 2)$ has been obtained via the Fisher's information. This controls both chemical and physical properties of some molecular systems. The Fisher information is considered only for $x>0$ due to the singular point at $x=0$. We found that Fisher-information-based uncertainty relation and the Cramer-Rao inequality holds. Some relevant numerical results are presented. The results presented shows that the Cramer-Rao and the Heisenberg products in both spaces provide a natural measure for anharmonicity of {$-V_0{\rm csch}^2(ax)$}

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B. J. Falaye, F. A. Serrano, Shi-Hai Dong. 2015-09-29. Fisher's information for the position-dependent mass Schrödinger system. https://doi.org/10.1016/j.physleta.2015.09.029

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