Abstract

Mesons are composed of one quark and one anti quark which are considered to be governed by quantum chromo
dynamic. In the present paper, it is considered that mesons are made up entirely, at least in principle, of light
quarks (u, d, s). Since mesons consisting of light quarks are relativistic systems, we cannot use the Schrödinger
equation, and the theory is rather limited. The light quark (u, d, s) mesons are intrinsically relativistic; because
binding energies (typically a few hundred MeV) are not small compared to the constituent masses. Therefore
they are based on nonrelativistic quantum mechanics. For the heavy quarks (c, b, t) though, the nonrelativistic
theory should work reasonably well. For most part of this paper we restricted our attention to relativistic bound
state of two particles and considered interaction between quark and antiquark, the essential point is that at short
range we expect a columbic potential and at large distance we have to account for quark confinement, the
simplest is a linear potential and other interaction oscillator potential. Then Dirac equation was solved with the
central potential analytically and the wave function of system was determined. Finally, by using wavefunction we
determined the charge radius of p0meson.

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