In this study, pentaquark P c 4380 composed of a baryon Σ c , and a D ¯ ∗ meson is considered. Pentaquark is as a bound state of two-body systems composed of a baryon and a meson. The calculated potential will be expanded and replaced in the Schrödinger equation until tenth sentences of expansion. Solving the Schrödinger equation with the expanded potential of Pentaquark leads to an analytically complete approach. As a consequence, the binding energy E B of pentaquark P c and wave function is obtained. The results E B will be presented in the form of tables so that we can review the existence of pentaquark P c . Then, the wave function will be shown on diagrams. Finally, the calculated results are compared with the other obtained results, and the mass of observing pentaquark P c and the radius of pentaquark are estimated.

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In this study, the bound state energy of a four-quark system was analytically calculated as a two heavy–heavy anti-quarks [Formula: see text] and two light–light quarks [Formula: see text]. Tetraquark was assumed to be a bound state of two-body system consisting of two mesons, each containing a light quark and a heavy antiquark. Due to the presence of heavy mesons in the tetraquark, Born–Oppenheimer approximation was used to study its bound states. To assess the bounding energy, Schrödinger equation was solved using lattice QCD [Formula: see text] potential, having expanded the tetraquark potential [Formula: see text] up to 11th term. Binding energy state and wave function, however, were obtained in the scalar [Formula: see text] channel. Graphical results for wave functions obtained versus antiquark–antiquark distance [Formula: see text] confirmed the existence of the tetraquark [Formula: see text]. Analytical bound state energy obtained here was in good agreement with several numerical ones published in the literature, confirming the accuracy of the approach taken here.

In this study, pentaquark P c (4380) composed of a baryon Σ c and a D * meson is considered. Pentaquark is as a bound state of two-body systems composed of a baryon and a meson. The calculated potential will be expanded and replaced in the Schrödinger equation until tenth sentences of expansion. Solving the Schrödinger equation with the expanded potential of Pentaquark leads to an analytically complete approach. As a consequence, the binding energy E B of pentaquark P c and wave function are obtained. The results E B will presented in the form of tables so that we can review the existence of pentaquark P c . Then, the wave function will be shown on diagrams. Finally, the calculated results are compared with another obtained results and the mass of observing pentaquark P c and the radius of pentaquark are estimated.