Asymptotic Iteration Method Solution of the Supersymmetric Schrödinger Equation (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.
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.
Numerical methods for solving radial Schrödinger equations
Journal of Computational and Applied Mathematics, 1989
An algorithm previously introduced by Brown et al. (1963) for solving radial Schrodinger equations is revisited and implemented in a more accurate way. The method is firstly applied to equations where potentials are present which are finite at the origin and which have an asymptotic behaviour V(r) + 0 as r + 00. Typical examples of potentials belonging to that class are the Woods-Saxon and the Morse potential. Furthermore the method is also used for Coulomb-like potentials such as the Hulthen and the Hellmann potential. A comparison between the approximated numerical values and other available numerical and exact bound state energies is made.
International Journal of Recent Advances in Physics, 2015
In this work, we obtained an approximate bound state solution to Schrodinger equation with modified Hylleraass plus inversely quadratic potential using Supersymmetric quantum mechanics approach. Applying perkeris approximation to the centrifugal term, we obtained the eigen-energy and the normalized wave function using Gauss and confluent hypergeometric functions. We implement Fortran algorithm to obtained the numerical result of the energy for the screening parameter 0.1, 0.2, 0.3, 0.4 0.5 and α =. The result shows that the energy increases with an increase in the quantum state. The energy spectrum shows increase in angular quantum state spacing as the screening parameter increases.