The Klein–Gordon Equation with Modified Coulomb Potential Plus Inverse-Square–Root Potential in Three-Dimensional Noncommutative Space

  • Abdelmadjid Maireche Laboratory of physical and chemical materials, physics department, sciences faculty, university of M’sila, Algeria
Keywords: Klein-Gordon equation, Coulomb potential plus inverse-square–root potential, noncommutative space phase and Bopp’s shift method


In present work, the three-dimensional modified Klein-Gordon equation (MKGE) is analytically solved under modified Coulomb potential plus inverse-square–root potential, in the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The new energy shift (ground state, first excited state and excited state) is obtained via first order perturbation theory in the 3-dimensional noncommutative real space (NC: 3D-RS) symmetries instead of solving MKGE with the Weyl Moyal star product. It is found that the perturbative solutions of discrete spectrum for studied potential depended on the parabolic cylinder functions, the Gamma function, the discreet atomic quantum numbers  and the potential parameters (and), in addition to noncommutativity parameters (and).


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Author Biography

Abdelmadjid Maireche, Laboratory of physical and chemical materials, physics department, sciences faculty, university of M’sila, Algeria

Laboratory of physical and chemical materials, physics department, sciences faculty, university of Mila, Algeria


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How to Cite
Maireche, A. (2019). The Klein–Gordon Equation with Modified Coulomb Potential Plus Inverse-Square–Root Potential in Three-Dimensional Noncommutative Space. To Physics Journal, 3, 186-196. Retrieved from
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