Schrödinger Equation with the Potential V(r)=a r²+b r^-4+c r^-6

1998/08/21 by Shi-Hai Dong, Dong, Shi-Hai, Xi-wen Hou +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9808037

PS file 10 pages, Submitted to J.P.A

arxiv created 1998/08/21 · arxiv updated 2009/12/01

Abstract

By making use of an \it ansatz for the eigenfunction, we obtain the exact solutions to the Schrödinger equation with the anharmonic potential, V(r)=a r²+b r^-4+c r^-6, both in three dimensions and in two dimensions, where the parameters a, b, and c in the potential satisfy some constraints.

Related

• Exact Solutions to the Schrödinger Equation for the Inverse-Power Potential in Two Dimensions
• Exact Solutions of the two-dimensional Schrödinger equation with certain central potentials
• A note on a class of exact solutions for a doubly anharmonic oscillator
• Virial-ansätze for the Schrödinger Equation with a symmetric strictly convex potential
• The Exact Solution to the Schrödinger Equation with the Octic Potential