The coset space representation is employed to study the algebraic molecular vibrational dynamics with SU(2) symmetry. The power of the coset space representation is that with it the quantum effect of the dynamics can be retrieved. It is shown that when J 2 ⪢ J, where J is half the total boson number N of the vibrational system, the coset space representation reduces to the classical Heisenberg correspondence. A sample calculation of H 2O and O 3 systems shows that, for N < 10, the quantum effect neglected in the classical Heisenberg correspondence can be significant. This is evidenced by the different local-normal transitions in these two algorithms.