In the framework of quantum mechanics, we investigate muon channeling in the Si (200) crystal. The transverse energy levels and wave functions are obtained for the Pöschl-Teller and the Doyle-Turner potentials. Comparative analysis demonstrates that analytical results of calculations obtained on the base of the Pöschl-Teller potential are in a good agreement with the numerical results of calculations in the Doyle-Turner model for the low energy levels. These results for the muon with rest mass m µ and relativistic factor γ are valid for any particle with elementary charge and rest mass m and relativistic factor γ m = γ(m µ /m). Therefore, our results can be useful for the preparation and performing the experimental investigation of the various phenomena accompanying particle channeling.