As quantum low-dimensional structures are of current interest, we tried to study the basic microscopic behaviour of electron subsystem in superlattices. The microtheoretical method of two-time temperature dependent Green’s fimctions was applied to calculate of electron energy spectra and spectral weights of electrons in superlattices (crystalline structures formed by alternating thin films with changed energy transfer between them). These analyses were performed combining the analytical (using the matrix representation of Chebishev’s polynomials) and numerical (using the programme Mathematics) approach leading to interesting results for the explanation of some physical properties of these structures.