Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method (original) (raw)
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Bound state solutions of the Schrödinger equation for modified Kratzer's molecular potential
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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 analytical solutions to the Kratzer potential by the asymptotic iteration method
International Journal of Quantum Chemistry, 2007
For any n and l values, we present a simple exact analytical solution of the radial Schrödinger equation for the Kratzer potential within the framework of the asymptotic iteration method (AIM). The exact bound-state energy eigenvalues (E nl ) and corresponding eigenfunctions (R nl ) are calculated for various values of n and l quantum numbers for CO, NO, O 2 , and I 2 diatomic molecules.
2
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.
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Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.
On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz
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Making an ansatz to the wave function, the exact solutions of the D -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the parameters of the given potential, δ and η are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D=3, we find that the bound state eigensolutions recover their standard analytical forms in literature.
Bound state solutions to the Schrödinger equation for some diatomic molecules
Pramana, 2018
The bound state solutions to the radial Schrödinger equation are obtained in three-dimensional space using the series expansion method within the framework of a general interaction potential. The energy eigenvalues of the pseudoharmonic and Kratzer potentials are given as special cases. The obtained analytical results are applied to several diatomic molecules, i.e. N 2 , CO, NO and CH. In order to check the accuracy of the present method, a comparison is made with similar results obtained in the literature by using other techniques.
Approximate Bound State Solutions for Certain Molecular Potentials
Journal of Applied Mathematics and Physics, 2021
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.
Int J Quantum Chem, 2000
ABSTRACT In this article exact solutions of a two-electron Schroedinger equation for the Coulomb potential were extended to the Fues-Kratzer-type potential: ({cflx Z}(Ω)/r) + ({cflx A}/r²). The wave function Ψ(r, Ω) is expanded into generalized Laguerre polynomials and hyperspherical harmonics. An analytical expression of two-electron systems is given for matrix elements and accurate energy eigenvalues of the excited state of {sup 1,3}S helium are calculated by using the hyperspherical harmonics method. The present results are compared with previous theoretical calculations and it is concluded that the convergence of energy eigenvalues is faster.