The pure qiiaiitum model d(\scril)ing lîahi oscillations of exciton-polaritons in a ınicro-cavity is consid(‘r(‘(l. IMiolon-c'Xcilon intiT’action Hamiltonian is diagonalized with the aid of Bogoliihov canonical transformations and polariton picture is obtained. We (ind that this picture is ecpiicalent to the two level atomsingle mode held interaction up to the lact that bosonic nature^ of this picture allows many i)articles in both level whose decays give radiation. We demonstrate tluit in contrast to tlie Jaynes-Cummings moded collapse and revivals cannot be seen in our model. Pumping mecluinism and its elfects on the preparation of the initial states are examined. It is found that initial statcîs of such system should form two-modi' coher('nt state'. Markovian da.iiiping is introduc('d in 1 h'isi'iibergLangevin formalism. It is shown that i 1h‘ (oscillations can Ix' obs('rv('d if cavity dtiinping rate does not excc'ed some critical value depending on coupling constant cind detuning (of cavity modex iLxplicit cxxjoii'ssion for la'iiormalized HaJoi frecpiency is found. Strong, weak and critical damioing r('giim‘s are studi('d in detciil.