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The Schr\"odinger-like equation written in terms of the displacement operatoris solved analytically for a inverse square plus Coulomb-like potential.Starting from the new Hamiltonian, the effects of the spatially dependent masson the bound states and normalized wave functions of the "usual" inverse squareplus Coulomb interaction are discussed.

Effective Mass Quantum Systems with Displacement Operator: Inverse Square plus Coulomb-like Potential