本文利用密度矩阵方法研究了柱形量子线中的光学克尔效应，重点讨论了电子－声子相互作用对其的影响，并以GaAs量子线为例进行了数值计算。结果显示，随着量子线半径R₀的减小，光学克尔效应会逐渐增强；考虑了电子－声子相互作用时的光学克尔效应比未考虑电子－声子相互作用时的大20%多；量子线半径R₀越小，峰越尖锐，峰值越强；当量子线半径R₀大于40nm时，峰会逐渐消失．

The optical Kerr effect in cylindrical quantum wires is investigated with density matrix approach,most emphasis is devoted to the electron-phonon interactions on the optical Kerr effect. With characteristic parameters pertaining to GaAs quantum wire,the numerical results are presented. It is shown that,the optical Kerr effect increases as the wire radius R₀ decreases;the optical Kerr considering the electron-LO-phonon interactions is over twenty percent greater than the one without considering the electron-phonon interactions;the smaller the wire radius R₀,the sharper the peak will be,and the larger the peak intensity will be;when the wire radius R₀ is greater than 40 nm,the peak will disappear gradually.