Algebraic method in calculations of nano-scaled objects properties

Abstract

The quantum mechanical calculations by means of the algebraic formulation are considered for the nano-scaled objects. The one-dimensional chain of one-dimensional quantum oscillators is selected as a model object sufficient for a range of solid state applications. In the calculations, well known algebraic formulation entities are used, such as the one-dimensional Morse quantum oscillator and the U(2) Lie algebra. The relative importance of the surface effects in the nano-scaled object is represented by considering both the radiation mechanisms and the difference in the behaviour of the quantum oscillator subchains having different lengths. The automation method for dealing with the numerically undetermined coupling parameters is suggested.