In the present work, we will introduce a way to obtain one model for the co
nductivity and the line-width function in a quasi two-dimensional quantum s
ystem. We choose the confinement potential to be a parabolic one. We will i
ntroduce a way to derive the line-shape formula by using of projectors. We
find some useful relations to calculate the line shape formula. Our result
shall be briefly compared with other results.