Schr\"{o}dinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$

Shi-Hai Dong; Xi-wen Hou; Zhong-Qi Ma

Schr\"{o}dinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$

Quantum Physics 2007-05-23 v1

Authors: Shi-Hai Dong , Xi-wen Hou , Zhong-Qi Ma

Abstract

By making use of an ${\it ansatz}$ for the eigenfunction, we obtain the exact solutions to the Schr\"{o}dinger equation with the anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$ , both in three dimensions and in two dimensions, where the parameters $a$ , $b$ , and $c$ in the potential satisfy some constraints.

Keywords

schrodinger equation anharmonic potential exact solution eigenfunction ansatz two-dimensional solution

Cite

@article{arxiv.quant-ph/9808037,
  title  = {Schr\"{o}dinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c r^{-6}$},
  author = {Shi-Hai Dong and Xi-wen Hou and Zhong-Qi Ma},
  journal= {arXiv preprint arXiv:quant-ph/9808037},
  year   = {2007}
}

Comments

PS file 10 pages, Submitted to J.P.A

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