PROBABILISTIC RADIAL ELECTRON DISTRIBUTION IN MOLECULAR SYSTEMS UNDER THE INFLUENCE OF KRATZER POTENTIAL USING THE PARAMETRIC NIKIFOROV-UVAROV
Abstract
Molecular systems influenced by the Kratzer potential have been investigated using the parametric Nikiforov-Uvarov method. This research aims to obtain the radial electron probability distribution of systems under the influence of the Kratzer potential without modifications, and to perform simulations of the radial probability distribution for oxygen, iodine, carbon monoxide, and nitrogen monoxide molecules. The radial electron probability distribution is obtained through the solution of the Schrodinger equation in the radial component. The radial component of the Schrodinger equation is obtained by separating the molecular system Schrodinger equation into three components: radial, zenithal, and azimuthal. The solution of the radial Schrodinger equation yields a radial wave equation, where the square of the absolute value provides the radial probability distribution of the electron's position with respect to the atomic nucleus. The solution to the radial component of the Schrodinger equation is achieved by applying the parametric Nikiforov-Uvarov method. Solving the radial component of the Schrodinger equation involves reducing the equation to a hypergeometric-type differential equation. Numerical computations and graphical simulations of the radial probability distribution are performed using the Matlab software. The research results indicate that the solutions for the radial electron probability distribution depend on spectroscopic parameters such as dissociation energy, equilibrium bond length, and molecular mass, as well as quantum numbers such as vibrational quantum number (n) and azimuthal quantum number (l). Iodine molecules exhibit the highest amplitude in the probability distribution plot compared to oxygen, carbon monoxide, and nitrogen monoxide.
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