The Exact Solution to the Schrödinger Equation with the Octic Potential

Details The Exact Solution to the Schrödinger Equation with the Octic Potential The Exact Solution to the Schrödinger Equation with the Octic Potential

1999-01-15

arxiv.org/abs/quant-ph/9901037v1

Physics

Quantum Physics

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

Scientific paper

The Schr\"{o}dinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schr\"{o}dinger 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 Schr\"{o}dinger equation with the octic potential, $V(r)=ar^2-br^4+cr^6-dr^4+er^{10}$.

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