The quantum dynamics of radiation propagating in a single mode optical fiber with Raman coupling to thermal phonons is analyzed. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum noise sources, including gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This allows quantum Langevin equations to be calculated, which have a classical form except for additional quantum noise terms. In practical calculations, it is more useful to transform to Wigner or +P quasi-probability operator representations. These result in complex-number stochastic equations, which can be analyzed using perturbation theory or exact numerical techniques.