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Approximate bound energies of diatomic molecules interactions by solving Schrodinger equation case of the modified Kratzer plus Hulthen potential

Khalid Reggab

Published Mar 29, 2024• 0 citations
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Abstract

Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.

DOI
10.21203/rs.3.rs-4163930/v1

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Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
The Schrödinger equation was solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov–Uvarov – functional analysis (NUFA) method. The bound-state energy and wave function for the HSKP were obtained in a closed form by applying the Greene–Aldrich approximation scheme to the inverse-square term. Using the resulting energy equation, we computed the energy spectra for 12 diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H2, ScH, CO, I2, N2, and NO) for various quantum states. To show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.
In this paper, we solved the Schrodinger equation with Hellmann-modified Kratzer potential using Nikiforov-Uvarov-Functional Analysis (NUFA) method. The obtained energy is used to study the numerical results of the ro-vibrational energy spectra for some selected diatomic molecules and their thermodynamic properties. In addition, we also investigated the Fisher information for three diatomic molecules and they all satisfied the Stam-Cramer-Rao inequalities uncertainty relations. Special cases of the potential are discussed and we compute the numerical eigenvalue of the modified Kratzer, Kratzer-Feus and Hellmann potentials for comparison with other analytical methods. The results of the present study agree with the results obtained with other known methods.
Abstract In this study, we investigated the approximate analytical bound state solutions of the Schrödinger equation, considering a linear combination of the deformed (Hulthén 1942 Ark. Mat. Astron. Fys. 28A 671) potential and the generalized (Kratzer 1920 Z. Phys. 3 289–307) potential. The analysis was performed within the path-integral formalism. Using an appropriate approximation to evaluate the centrifugal term, we derived the energy spectrum and normalized wave functions of the bound states from the poles of the Green’s function and its residues. To evaluate the accuracy and applicability of the derived expressions, we discuss several limiting cases of the potential and carry out numerical calculations of the energy levels, complemented by illustrative plots for selected diatomic molecules.
In this work, we proposed a screened modified Krazer potential and use the newly proposed Nikiforov-Uvarov-Functional Analysis (NUFA) method to obtain the energy spectrum and the corresponding wave function. With the obtained energy spectrum, we studied the numerical results for some selected diatomic molecules and our results are in good agreement with other analytical method. We also evaluated the vibrational partition function for , and diatomic molecules via the Euler–Maclaurin approach and other thermodynamic functions such as free energy, entropy, mean energy and specific heat Capacity. The expectations values of and are also calculated numerically for different diatomic molecules using the normalized wave function for the two low lying states corresponding to the ground and first excited states. Our numerical results for the selected diatomic molecules validate the Heisenberg uncertainty relation, .