The Analytical Solution of the Schr"odinger Particle in Multiparameter Potential (original) (raw)
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Journal of Physics B: Atomic, Molecular and Optical Physics, 2007
We present the exact and iterative solutions of the radial Schrödinger equation for a class of potential, V (r) = A r 2 − B r + Cr κ , for various values of κ from -2 to 2, for any n and l quantum states by applying the asymptotic iteration method. The global analysis of this potential family by using the asymptotic iteration method results in exact analytical solutions for the values of κ = 0, −1 and −2. Nevertheless, there are no analytical solutions for the cases κ = 1 and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with the previous works. PACS numbers: 03.65.Ge Keywords: asymptotic iteration method, eigenvalues and eigenfunctions, Kratzer, Modified Kratzer, Goldman-Krivchenkov, spiked harmonic oscillator, Coulomb plus linear and Coulomb plus harmonic oscillator potentials.
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.
Any l -state solutions of the Hulthén potential by the asymptotic iteration method
Journal of Physics A: Mathematical and General, 2006
In this article, we present the analytical solution of the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different δ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.
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.
Bound state solutions of the Hulthén potential by using the asymptotic iteration method
Physica Scripta, 2007
We present very accurate values for the bound state energy eigenvalues by solving the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method (AIM) for any states and for different screening parameters without using any approximations required by other methods. The AIM results are compared with the results of the numerical integration, the generalized pseudospectral, the supersymmetry, the variational and the shifted 1/N expansion methods and they are in very good agreement for different screening parameter, δ, values.
Approximate solutions of Schrödinger equation for Eckart potential with centrifugal term
Chinese Physics B, 2010
The approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ = λ = 1, and β = 0, are investigated.
On numerical solution of the Schrödinger equation: the shooting method revisited
Computer Physics Communications, 1995
An alternative formulation of the "shooting" method for a numerical solution of the Schr0dinger equation is described for :ases of general asymmetric one-dimensional potential (planar geometry), and spherically symmetric potential. The method relies on matching the asymptotic wavefunctions and the potential core region wavefunctions, in course of finding bound states energies. It is demonstrated in the examples of Morse and Kratzer potentials, where a high accuracy of the calculated eigenvalues is found, together with a considerable saving of the computation time.
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.