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Pg. 240-251
Energy Eigenvalues and Eigen functions of a Diatomic Molecule in Quadratic Exponential-type Potential
1Eyube E.S., 2Wadata Umar, and 3Najoji Sunday David 1Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria 2Department of Physics, School of Sciences, Aminu Saleh College of Education, Azare, Nigeria 3Department of Basic Sciences, School of General and Remedial Studies, Federal Polytechnic Damaturu, Damaturu, Nigeria 1 Corresponding Author: edwineyubes@mautech.edu.ng;
Abstract
We employed the exact quantization rule to obtain closed form expression for the bound state energy eigenvalues of a molecule in quadratic exponential-type potential. To deal with the spin-orbit centrifugal term of the effective potential energy function, we have used a Pekeris-type approximation scheme, we have also obtained closed form expression for the normalized radial wave functions by solving the Riccati equation with quadratic exponential-type potential. Using our derived energy eigenvalue formula, we have deduced expressions for the bound state energy eigenvalues of the Hulthén, Eckart and Deng-Fan potentials, considered as special cases of the quadratic exponential-type potential. Our deduced energy eigenvalues are in excellent agreement with those in the literature. We have computed bound states energy eigenvalues for six diatomic molecules viz: HCl, LiH, H , SeH, VH and TiH. Our results are in total agreement with existing 2 results in the literature for the s-wave and in good agreement for higher quantum states. By solving the Riccati equation, we have obtained normalized radial wave functions of the quadratic exponential-type potential, our results show higher probabilities of finding the molecule in the region 0.1 ≤ y ≤ 0.2
Key words: eigenvalues, eigen functions, quadratic exponential-type potential, exact quantization rule, Riccati equation
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