Solutions of the Schrodinger equation of the shifted screened Kratzer potential and its thermodynamic functions using the extended Nikiforov–Uvarov method (original) (raw)
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In this study, the Schrödinger equation with the Hulthén plus screened Kratzer potentials (HSKP) are solved via the Nikiforov-Uvarov (NU) and the series expansion methods. We obtained the energy equation and the wave function in closed form with Greene-Aldrich approximation via the NU method. The series expansion method was also used to obtain the energy equation of HSKP. Three distinct cases were obtained from the combined potentials. The energy eigenvalues of HSKP for HCl, LiH, H2, and NO diatomic molecules were computed for various quantum states. To test the accuracy of our results, we computed the bound states energy of HCl and LiH, for a special case of Kratzer and screened Kratzer potentials, which are in excellent agreement with the report of other researchers.
Analytical Solutions of the Molecular Kratzer-Feus potential by means of the Nikiforov-Uvarov Method
Journal of Mathematical Chemistry
The analytical methods for solving Schrödinger equation are essential and effective tools with which we can investigate the spectroscopic properties, the electronic structure, and the energetic properties of the diatomic molecules (DMs). Accordingly, in this work, we used the Nikiforov-Uvarov (NU) method to solve the three-dimensional nonrelativistic Schrödinger equation with the molecular Kratzer-Feus (KF) potential and obtain the exact analytical bound state energy eigenvalues as well as their corresponding normalized eigenfunctions. The effective KF diatomic molecular potential well is investigated and represented graphically for several well-known DMs. The bound state energy levels are tabulated numerically for arbitrary values of the vibrational and rotational quantum numbers. The results obtained in this work are found to be in excellent agreement with the already-existing results in the literature.
Eigensolutions and Thermodynamic Properties of Kratzer plus generalized Morse Potential
2022
In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrödinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation were use to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.PACS Nos: 03.65Ge; 03.65-w; 03.65Ca
2012
We obtain the bound-state solutions of the radial Schr\"odinger equation (SE) with the shifted Deng-Fan (sDF) oscillator potential in the frame of the Nikiforov-Uvarov (NU) method and employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding wave functions are obtained for arbitrary -state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.
Vibrational energies of some diatomic molecules for a modified and deformed potential
2021
A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov-Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.
Ro-vibrational studies of diatomic molecules in a shifted Deng-Fan oscillator potential
International Journal of Quantum Chemistry, 2014
Bound-state spectra of shifted Deng-Fan oscillator potential are studied by means of a generalized pseudospectral method. Very accurate results are obtained for both low as well as high states by a non-uniform optimal discretization of the radial Schrödinger equation. Excellent agreement with literature data is observed in both s-wave and rotational states. Detailed variation of energies with respect to potential parameters is discussed. Application is made to the ro-vibrational levels of four representative diatomic molecules (H 2 , LiH, HCl, CO). Nine states having {n, ℓ} = 0, 1, 2 are calculated with good accuracy along with 15 other higher states for each of these molecules.
Bound state solutions of the Schrödinger equation for modified Kratzer's molecular potential
Chemical physics letters, 2006
The energy spectra and the wave function depending on the c-factor are investigated for a more general Woods-Saxon potential (MGWSP) with an arbitrary-state. The wave functions are expressed in terms of the Jacobi polynomials. Two potentials are obtained from this MGWSP as special cases. These special potentials are Hulthen and the standard Woods-Saxon potentials. We also discuss the energy spectrum and wave function for the special cases.
Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules
Journal of Mathematical Chemistry, 2009
For any arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D ≥ 2) hyperradial Schrödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact energy levels (E nl) of all the bound-states are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (ψ nl (r)) are also calculated. The exact energy eigenvalues for these Kratzer-type potentials are calculated numerically for the typical diatomic molecules LiH, CH, HCl, CO, N O, O 2 , N 2 and I 2 for various values of n and l quantum numbers. Numerical tests using the energy calculations for the interdimensional degeneracy (D = 2 − 4) for I 2 , LiH, HCl, O 2 , N O and CO are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.