Alarge number of researches have shown that the low dimensional semiconductor materials are the ideal nonlinear optical materials.With the progress of crystal growth technology

many low dimensional quantum systems with different dimensions and sizes can be fabricated.So the nonlinear optical effects in the low dimensional semiconductor materials become the important research aspects.Analytic formulas for the linear and third-order nonlinear changes in the index of the refraction are obtained for Morse quantum wells by the compact density matrix method and the iterative procedure.The numerical results are presented for a typical GaAs/A1GaAs Morse quantum wells.The numerical results reveal that

the linear refractive index changes are not related to the incident optical intensity.However

the incident optical intensity has a striking influence on the third-order nonlinear refractive index changes.When the incident optical intensity increased

the total refractive index change will reduce.When the parameter increased

the total refractive index changes will decrease.When the carrier density increases

the total refractive index changes will increase.By contrast

it can be seen that the total refractive index changes equals to zero at the peak value of the optical Absorption.So the large changes in the index of refraction can be obtained when the optical Absorption is small.