||We analyzed a weak value amplification of single photon nonlinearity exactly. Since the cross-phase modulation (XPM) between a single photon and the probe beam is very small, the measurement of the phase shift of the probe beam is difficult. Feizpour et al. have shown that the photon number in the interferometer can be amplified by pre- and post-selection, and weak measurements. As a result of the weak value amplification of the photon number, the phase shift of the probe light is also amplified, therefore, SNR, which is limited by technical noise, can be improved. Feizpour et al. showed that the amplification of the phase shift is occurred by using the approximation on condition of the weak interaction between the single photon and the probe beam. In this paper, we calculate the post-selected state of the probe beam exactly. Moreover, we calculated the fidelity between the post-selected probe state and the squeezed coherent state, and the probability density distribution of the post-selected probe state. As a result, the phase shift is amplified more greatly than the value expected from the theory of the weak value. Furthermore, the state of the probe beam is 2.6dB-squeezed by the post-selection.