We consider the quantum Lorentz gas (QLG) in the plane. We show that the spectral properties of the quantum Lorentz gas can be obtained from the study of a homogeneous system of one-dimensional integral equations. The qualitative spectral analysis is performed, and the spectrum is shown to have a band structure. The wave functions in the complete configuration space can be constructed in terms of the solutions of the obtained effective equations. We apply the obtained result to a simpler Lorentz gas model including additional symmetry.