#### Research Articles

# Solutions of Klein-Gordon equation for the modified central complex potential in the symmetries of noncommutative quantum mechanics

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**Author:**

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Abdelmadjid Maireche

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University of M'sila, DZ

##### About Abdelmadjid

Laboratory of Physics and Material Chemistry, Physics department, Sciences Faculty

## Abstract

We explore the new analytical solutions for both bound and the new masses of mesons of the Klein–Gordon equation with the modified central complex potential, which describes the heavy light *Ǭq*, (*Q *= *c*, *q *= *u*/*d*, *s*) mesons and the quarkonium system *ǭǭ*, (q=c, b, s) via the standard Bopp’s shift method and standard perturbation theory.We have obtained the energy eigenvalues of the ground state *E*^{(0)}_{nc}(a, b, 0, *j, l, m)* the first excited state *E*^{(1)}_{nc}(a, b, 1, *j, l, m*) and *p*^{th} the excited state *E*^{(p)}_{nc}(a, b, p, j, l, m) in terms of the shift energy (Δ*E*_{cc}(0*, j, l, s, m*), Δ*E*_{cc}(1,*j,l,s,m*) and Δ*E*_{cc}(*p, j, l, s, m*) and *(E*_{0l}*, E*_{1l}* and E*_{nl})) of ordinary relativistic quantum mechanics. In addition to the parabolic cylinder functions, the Gamma function, the discreet atomic quantum numbers (*j, l, s, m*)* *the potential parameters (*a *and *b*) and the noncommutativity parameters (θ and σ). In the second part of the research, we will apply the obtained results to calculate the new masses of the mentioned previously mesons in the symmetries of the relativistic three-dimensional noncommutative quantum mechanics. Moreover, some important special cases in the context of the symmetries of the relativistic three-dimensional noncommutative quantum mechanics are treated.
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How to Cite:
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Maireche, A., 2021. Solutions of Klein-Gordon equation for the modified central complex potential in the symmetries of noncommutative quantum mechanics. *Sri Lankan Journal of Physics*, 22(1), pp.1–19. DOI: http://doi.org/10.4038/sljp.v22i1.8079
Published on
09 Jan 2021.

Peer Reviewed

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