  We revisit the scheme of single-photon weak-coupling optomechanics using
post-selection, proposed by Pepper, Ghobadi, Jeffrey, Simon and Bouwmeester
[Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the
dynamical evolution. Positive and negative amplification effects of the
displacement of the mirror's position can be generated when the Kerr phase is
considered. This effect occurs when the post-selected state of the photon is
orthogonal to the initial state, which can not be explained by the usual weak
measurement results. The amplification effect can be further modulated by a
phase shifter, and the maximal displacement state can appear within a short
evolution time.
