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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

M. Aygun·O. Bayrak·I. Boztosun
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Abstract

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

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M. Aygun, O. Bayrak, I. Boztosun. 2007-03-13. 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. https://doi.org/10.1088/0953-4075/40/3/009

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