An analytical approach for determine the acoustic phonon dispersion relation in the qusi-2D nanosystems such as flat ultra-thin flat films is represented there. Method is based on the representation the components of polarization vectors for all possible phonon branches in the film of finite thickness as appropriate Fourier series. This made it possible to establish the analytical dependencies of energy on the frequency for all branches of the acoustic phonon spectrum in ultra-thin films. Such results can allow an analytical investigations of the electron spectra transformations that caused by electrons interaction with acoustic phonons in the ultra-thin films by variation of their thicknesses.
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