The Exact Solution to the Schrödinger Equation with the Octic Potential

1999/01/15 by Shi‐Hai Dong, Shi-Hai Dong, Dong, Shi-Hai +2
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9901037

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

arxiv created 1999/01/15 · openalex publication_date 1999/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)=ar²-br⁴+cr⁶-dr⁴+er¹⁰.

Citations

• The Principles of Quantum Mechanics

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