ON THE BOUND STATE EQUATION OF MESONS AND ITS SOLUTIONS

A possible bound state equation of mesons is proposed, which is an integral equation of the Bethe-Salpeter type, and is relativistically covariant. The integral kernel in the equation is not the one as given by the ladder approximation, but is introduced phenomcnologically in accordance with the super strong interaction of a potential well type. Under the approximation of the straton model, the bound state equation of mesons is expanded in terms of four dimensional spherical harmonics and numerical solutions are obtained on a computer. It is found that there exist two kinds of solutions: the ground state solution and the excited state solution. The wave function of the latter solution oscillates in the configuration space, corresponding to an average potential well with a large area. The calculation results show that only potential well with a very flat bottom could lead to a bound state wave function of mesons with large average radius as evidenced by experimental results.