In order to inspect the reliability level of the approximate wave function in molecular physics,we calculated the approximate wave function and the potential energy of the ground state of H₂⁺.We studied the effect of approximate wave function of ground state of H₂⁺ on its potential energy.We got accurate equilibrium position by comparing with RKR potential when z=1.23,but on higher vibrational levels z=1.16 is very well.