Finally, in order to illustrate the classical-quantum correspondence we explain the differences in the extent of cavity-mediated isomerization for the three initial states in Fig. (a) due to the participation of specific polariton states and their phase space nature. We obtain the polariton states by diagonalizing the Hamiltonian using the Fourier grid Hamiltonian method with the usual convergence criteria in terms of varying the grid spacing and size . The initial states are then written in terms of the linear combination of the polariton states