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Analytical Solution of Conformable Schro ̈dinger Wave Equation with Coulomb Potential |
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PP: 137-147 |
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doi:10.18576/pfda/100113
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Author(s) |
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Mohamed Ghaleb Al-Masaeed,
Eqab.M.Rabei,
Ahmed Al-Jamel,
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Abstract |
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| In this paper, the conformable equation for hydrogen-like systems with conformable Coulomb’s potential is constructed. Then, the conformable eigenfunctions and energy eigenvalues are obtained. The analytic solutions are expressed in terms of conformable spherical harmonics and conformable Laguerre functions that are appeared and defined in this work. Some aspects of the results are discussed. For instance, the probability density for the first three levels and different values of α are plotted, and it is observed that the probability density gradually converts to α = 1 for all levels. The traditional version of this problem is recovered when the fractional parameter α = 1. The set of conformable eigenfunctions could be useful as a basis for approximation methods developed for the conformable counterparts that appeared in conformable quantum mechanics.
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