Exact Solutions of the two-dimensional Schrödinger equation with certain central potentials

2000/03/22 by Shi‐Hai Dong, Shi-Hai Dong, Dong, Shi-Hai
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0003100

Latex files and accepted by Inter. J. Theor. Phys. 39, No. 4

arxiv created 2000/03/22 · openalex publication_date 2000/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By applying an ansatz to the eigenfunction, an exact closed form solution of the Schrödinger equation in 2D is obtained with the potentials, V(r)=ar²+br⁴+cr⁶, V(r)=ar+br²+cr^-1 and V(r)=ar²+br^-2+cr^-4+dr^-6, respectively. The restrictions on the parameters of the given potential and the angular momentum m are obtained.

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