A comprehensive and detailed investigation is presented on the dynamics of the lower hybrid wave during current drive in tokamaks in situations where toroidally induced ray stochasticity is important and on the Weyl-Wigner formalism for rotation angle and angular momentum variables in quantum mechanics. It is shown that ray-tracing and Fokker-Planck codes are reliable tools for modelling the physics of lower-hybrid current drive provided a large number of rays is used when stochastic effects are important, and, in particular, that such codes are capable of reproducing the experimentally observed features of the hard X-ray emission. The balance between the wave damping and the stochastic divergence of nearby ray trajectories appears to be of great importance in governing the dynamics of the launched power spectrum and in establishing the characteristics of the deposition patterns. The implications of rotational periodicity and of angular momentum quantization for the Weyl-Wigner formalism are analyzed. Particular attention is paid to discreteness and its consequences: importance of evenness and oddness, use of two difference operators instead of one differential operator. 24 refs.