The Exact Solution to the Schrödinger Equation with the Octic Potential

Shi-Hai Dong, Zhong-Qi Ma

备注：: Latex file 9 pages and submit to J. P. A

英文摘要：

The Schrödinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schrödinger equation for the radial wave function through a simple transformation. As an example, applying an ${\it ansatz}$ to the eigenfunctions, we then arrive at an exact closed form solution to the modified two-dimensional Schrödinger equation with the octic potential, $V(r)=ar^2-br^4+cr^6-dr^4+er^{10}$.

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