In connection with the experimental result which stated that polyethylene foil amplifies about three times the penetrated light, we propose two theoretical explanations of this phenomenon. One of them is that several amplified peaks are the consequence of the forming of solitons in a polyethylene chain whose velocities are close to the velocity of sound. Forming of solitons, together with boundary conditions in a polyethylene macromolecules chain, which contain about thirty monomers, lead to the amplification of light. The second explanation requires introduction of homeopolar excitons in polymer macromolecules. Both energy gap of homeopolar excitons and width of homeopolar exciton zone are of the same order of magnitude. It means that transitions in a very wide zone give light quanta which are able to amplify the initial light. In order to avoid some confusion and misunderstandings, we wish to point out the following. Atoms and molecules as the whole are treated classically (transition through potential barriers, for example, etc.). The exception to this rule are phonon theories of crystals where the phonon is considered as a quanta of boson field, i.e., it means that, in the theory of mechanical oscillations, molecules and atoms as the whole are treated quantum mechanically. On the other hand, elementary excitations in crystals such as excitons, vibrons, spin waves, and ferroelectric excitations, etc., which arise from changes of some parts of atoms or molecules are treated quantum mechanically exclusively. In the analyses of this work, the excitations of an individual molecule subsystem (i.e. the quantum objects) would serve as an explanation of the light amplification by a polymer chain