We report here the complete eigenvalue structure and the corresponding eigenfunctions of the neutron transport operator for the neutron wave propagation through water and heavy water. The calculations have been performed in multi-group diffusion theory approximation using realistic scattering kernels. The results are found to be rather insensitive to the chemical binding effects. The bounds on the eigenvalues have also been discussed and the results corresponding to the fundamental mode eigenvalue have been compared with the experimental data for heavy water. Our results show that there exists only one resolvable mode for water and four resolvable modes for heavy water.