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

Abstract

This study presents the Fisher information for the position-dependent mass Schrödinger equation with hyperbolical potential {$V(x)=-V_0{\mathrm{csch}}^2(ax)$}. 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 {$-V_0{\mathrm{csch}}^2(ax)$}

References in corpus (1)

• Eigensolution techniques, their applications and the Fisher's information entropy of Tietz-Wei diatomic molecular model

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