We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1 AЈ state ͓J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 ͑1998͔͒, the 3 AЈ and the two degenerate 3 AЉ states ͓S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 ͑2000͔͒, and the spin-orbit couplings between them ͓B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 ͑2003͔͒. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state ⌸ 3/2 to ⌸ 1/2 of the product OH was calculated to be ϳ2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.