The quasi-exact Bethe Ansatz method, has been examined for solving radial Schr¨odinger equation with Yukawa potential, as an important central interaction for computing bound states of neutral atoms. The method, in spite of its simplicity with respect to other methods, leads to the ground state and low excited states of radial Schr¨odinger equation with a good accuracy. It is found that the results are generally in agreement with the results of others and therefore, this method can be used for solving Schr¨odinger equation instead of other numerical and analytical methods. It was also found that the energy eigenvalues reach to that of coulomb potential in the limit of zero screening parameter. The method has been briefly generalized to arbitrary dimension for Yukawa potential inspiring the 3-Dimensional trail wave function.
