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

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

2007-03-13

arxiv.org/abs/math-ph/0703040v1

J Phys B: Atomic, Molecular and Optical Physics 40 (2007) 537

Physics

Mathematical Physics

12 pages and 5 tables

Scientific paper

10.1088/0953-4075/40/3/009

We present the exact and iterative solutions of the radial Schr\"{o}dinger equation for a class of potential, $V(r)=\frac{A}{r^{2}}-\frac{B}{r}+Cr^{\kappa}$, 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.

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