Solution of the Radial Schrödinger Equation for the Potential Family $V(r)=\frac{A}{r^2}-\frac{B}{r}+C{r}^{\kappa }$ using the Asymptotic Iteration Method

Abstract

We present the exact and iterative solutions of the radial Schrödinger equation for a class of potential, $V(r)=\frac{A}{r^2}-\frac{B}{r}+C{r}^{\kappa }$, for various values of $\kappa$ 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 $\kappa =0,-1$ and -2. Nevertheless, there are no analytical solutions for the cases $\kappa =1$ and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with the previous works.

arXiv comment12 pages and 5 tables

References in corpus (6)

• Asymptotic iteration method for eigenvalue problems
• Perturbation theory in a framework of iteration methods
• Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
• Asymptotic Iteration Method Solutions to the Relativistic Duffin-Kemmer-Petiau Equation
• Simple strong glass forming models: mean-field solution with activation
• Coulomb plus power-law potentials in quantum mechanics

Cited by in corpus (8)

• Eigensolution techniques, their applications and the Fisher's information entropy of Tietz-Wei diatomic molecular model
• Formula Method for Bound State Problems
• Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential
• An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems
• An alternative solution of Diatomic Molecules
• Intrinsic Classes in the Union of European Football Associations Soccer Team Ranking
• Discrete Fractional Solutions of a Physical Differential Equation via $\nabla$-DFC Operator
• A simple model potential for hollow nanospheres