Bound state solutions of the Schrödinger equation for reducible potentials: general Laurent series and four-parameter exponential-type potentials (original) (raw)
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Il Nuovo Cimento B, 1999
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We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene-Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.
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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.
Annalen der Physik, 2009
A new approximation scheme to the centrifugal term is proposed to obtain the l = 0 bound-state solutions of the Schrödinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter σ 0. Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave (l = 0) and σ 0 = 1 cases are given.
2008
A new approximation scheme to the centrifugal term is proposed to obtain the l≠ 0 bound-state solutions of the Schrödinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter σ_0. Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave (l=0) and σ_0=1 cases are given.
EIGENSOLUTIONS OF THE SCHRӦDINGER EQUATION WITH A COMBINATION OF SIMILAR POTENTIALS.pdf
The approximate analytical solutions of the non-relativistic Schrӧdinger equation with a combination of three potentials in any arbitrary states is solved using a suitable approximation scheme to the centrifugal barrier. The energy eigenvalue equation and the corresponding wave function are obtained in a closed and compact form using the powerful methodology of parametric Nikiforov-Uvarov method. By changing the numerical value of each of the potential strength, we deduced the energy equation for some well-known poten als. Using MATLAB 7.5.0.342 programing, we obtained the numerical results for each of the deduced potential. It is observed that the numerical results for each of these potentials are equivalent. Finally, we observed that the strength of the Coulomb potential and that of the Yukawa potential have the same effects on the energy.
2020
In this paper, we obtained the exact bound state energy spectrum of the Schrodinger equation with energy dependent molecular Kratzer potential using asymptotic iteration method (AIM). The corresponding wave function expressed in terms of the confluent hypergeometric function was also obtained. As a special case, when the energy slope parameter in the energy-dependent molecular Kratzer potential is set to zero, then the well-known molecular Kratzer potential is recovered. Numerical results for the energy eigenvlaues are also obtained for different quantum states, in the presence and absence of the energy slope parameter. These results are discussed extensively using graphical representation. Our results are seen to agree with the results in literature.
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.