Eigensolution techniques, expectation values and Fisher information of Wei potential function
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ORIGINAL PAPER
Eigensolution techniques, expectation values and Fisher information of Wei potential function C. A. Onate 1
&
M. C. Onyeaju 2 & D. T. Bankole 1 & A. N. Ikot 2
Received: 19 May 2020 / Accepted: 15 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract An approximate solution of the one-dimensional relativistic Klein-Gordon equation was obtained under the interaction of an improved expression for Wei potential energy function. The solution of the non-relativistic Schrödinger equation was obtained from the solution of the relativistic Klein-Gordon equation by certain mappings. We have calculated Fisher information for position space and momentum space via the computation of expectation values. The effects of some parameters of the Wei potential energy function on the Fisher information were fully examined graphically. We have also examined the effects of the quantum number n and the angular momentum quantum number ℓ on the expectation values and Fisher information respectively for some selected molecules. Our results revealed that the variation of most of the parameters of the Wei potential energy function against the Fisher information does not obey the Heisenberg uncertainty relation for Fisher information while that of the quantum number and angular momentum quantum number on Fisher information obeyed the relation. Keywords Eigensolutions . Wave equations . Klein-Gordon equation . Fisher information . Expectation value . Potential function
Introduction In order to find the properties of some quantum mechanical systems in the non-relativistic sector, one needs to solve the Schrödinger wave equation which in the time evolution describes either the time-dependent or time-independent solutions. Most studies carried out by uncountable number of authors focused on the solution of time-independent counterpart of the Schrödinger equation for various physical potentials of interest. Some of the potentials reported unfortunately have centrifugal term which demands the use of an approximation scheme to conveniently deal with the centrifugal term. Such potentials include the Yukawa potential, Coulomb potential, Hellmann potential and Frost-Musulin potential. The choice of the proper approximation scheme to the centrifugal term is always a constraint to the authors. However, in the atomic domain, some of these potentials cannot be used to study/ * C. A. Onate [email protected] 1
2
Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Port Harcourt, Nigeria
describe diatomic molecules. Thus, there is a little diversion of interest towards the empirical potential energy function for diatomic molecules [1–15]. This is because the potential function provides the most compact way to summarize our understanding of a molecule. Recently, Jia et al. [16] modified some already existing molecular potential energy functions, which are now referred to as the improved expressions fo
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