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The Exact Solution to the Schrödinger Equation with the Octic Potential

Shi-Hai Dong·Zhong-Qi Ma
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Abstract

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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Shi-Hai Dong, Zhong-Qi Ma. 1999-01-15. The Exact Solution to the Schrödinger Equation with the Octic Potential. https://arxiv.org/abs/quant-ph/9901037

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