Bound state solutions, Fisher information measures, expectation values, and transmission coefficient of the Varshni potential

The eigensolutions of the Schrodinger equation under the Varshni potential function are studied with two eigensolution techniques such as the Nikiforov- Uvarov and the semi-classical WKB approximation methods. We extended the work to investigate the analytical and numerical Fisher information measure of complexities and also the expectations values using the Hellmann-Feynman theorem. Wedetermined the transmission coefficient using the WKB method. The WKB energy levels andmeanvalues fluctuate with the potential range compared with theNUderived values. Our results for the Fisher information measure obey the uncertainty relation I(rho)I(gamma) >= 36 and the Cramer-Rao inequality for position space (I(rho) < r(2)> >= 9). The mean values conform to the ones reported in existing literature. [GRAPHICS] .

Automated summary

The eigensolutions of the Schrodinger equation under the Varshni potential function were studied using the Nikiforov-Uvarov and the semi-classical WKB approximation methods. The analysis was extended to investigate the Fisher information measure and expectations values, along with the transmission coefficient using the WKB method. Results showed fluctuations in WKB energy levels and mean values compared with NU-derived values, along with compliance to certain uncertainty relations and inequalities for position space.