Abdelmadjid Maireche, A New Nonrelativistic Investigation for the Lowest Excitations States of Interactions in One-Electron Atoms, Muonic, Hadronic and Rydberg Atoms with Modified Inverse Power Potential, IFSL Volume 9, International Frontier Science Letters (Volume 9)
https://www.scipress.com/IFSL.9.33
Abstract:
    A new theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems at low energy for modified inverse power potential (m.i.p.) is discussed by means Boopp’s shift method instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms, muonic, hadronic and Rydberg atoms by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters (<i>θ,χ</i>) and (<i>θ,σ</i>), which are induced by position-position and momentum-momentum noncommutativity, in addition to the discreet atomic quantum numbers (<i>j</i>=<i>l</i>±1/1, <i>s</i>=±1/2 and <i>m</i>) and we have also shown that, the old states are canceled and has been replaced by new degenerated 4(2<i>l</i>+1) sub-states.
Keywords:
    Boopp’s Shift Method, Hadronic Atoms, Inverse Power Potential, Muonic Atoms, Noncommutative Phase, Noncommutative Space, Rydberg Atoms, Star Product