Abstract
A novel study for the exact solvability of nonrelativistic quantum spectrum systems for companied Harmonic oscillator potential and its inverse (the isotropic harmonic oscillator plus inverse quadratic potential) is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), furthermore the exact corrections for the spectrum of studied potential was depended on two infinitesimals parameters θ and θ¯ which plays an opposite rolls, this permits us to introduce a new fixing gauge condition and we have also found the corresponding noncommutative anisotropic Hamiltonian.
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