Exact Solution of Schrödinger Equation for Pentaquark Systems

Abstract

‎In this paper‎, ‎we present an exact analytical solution for five interacting quarks‎. ‎We solve the Schr\"{o}dinger equation for pentaquarks in the framework of five-body and two-body problems‎. ‎For this purpose‎, ‎we utilize Yukawa potential in Jacobi coordinates‎. ‎Also finding the relation between the reduced masses and coupling constants of pentaquarks‎, ‎we obtain the coupling constant of Yukawa potential for pentaquark systems‎. ‎We calculate the energy of these systems in their ground state‎. ‎The results are well consistent with the theoretical results‎. ‎Our procedure to obtain these results is appropriate for other potentials and $n$-body systems‎.

Keywords

• exact solution
• schrödinger equation
• pentaquark
• coupling constant
• yukawa potential