Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum

Details Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum

2005-10-25

arxiv.org/abs/quant-ph/0510193v1

Physics

Quantum Physics

44 pages for text, 3 figures

Scientific paper

10.1016/j.aop.2005.11.009

We present an explicit convergent iterative solution for the lowest energy
state of the Schroedinger equation with an $N$-dimensional radial potential
$V=\frac{g^2}{2}(r^2-1)^2$ and an angular momentum $l$. For $g$ large, the rate
of convergence is similar to a power series in $g^{-1}$.

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