Abdelmadjid Maireche, A New Study to the Schrödinger Equation for Modified Potential V(r)=ar2+br-4+cr-6 in Nonrelativistic Three Dimensional Real Spaces and Phases, Volume 61, International Letters of Chemistry, Physics and Astronomy (Volume 61)
https://www.scipress.com/ILCPA.61.38
Abstract:
    In present work, by applying Boopp’s shift method and standard perturbation theory we have generated exact nonrelativistic bound states solution for a modified potential (see formula in paper) in both three dimensional noncommutative space and phase (NC: 3D-RSP) at first order of two two infinitesimal parameters antisymmetric (see formula in paper), we have also derived the corresponding noncommutative Hamiltonian.
Keywords:
    Anharmonic Potential, Boopp’s Shift Method, Harmonic Potential, Noncommutative Phase, Noncommutative Space, Schrödinger Equation, Star Product