中文摘要：

利用求解能量本征方程、幺正变换及变分相结合的方法，研究了纳米管中极化子的性质。数值计算结果表明：极化子基态和第一激发态能量随纳米管内径的增大或外径的减小而增大，说明纳米管具有明显的量子尺寸效应；随电子．声子间耦合强度的增大而减小。电子．声子之间的相互作用导致电子和声子相互作用能的绝对值增大，进而导致极化子的能量减小；随纳米管方向波矢的增大而增大。该方向波矢增大，电子的动能增大，则极化子能量增大。

英文摘要：

The properties of polaron in nanotubes are invesgated by combination of solving the energy eigen-equation, unitary transformation and variation method. Numerical calculation results indicate that the energy of ground state and first excited state of polaron increases with increasing nanotube inside radius or decreasing nanotube outside radius, which illustrates that the nanotubes have obvious quantum size effect. It decreases with increasing of the electron-phonon coupling strength. The interaction between the electron and phonon leads to the absolute value increasing of interaction energy and decreasing of the polaron energy. It increases with increasing wave vector along the nanotube orientation. Increasing wave vector of the direction leads to increasing of the electron kinetic energy, and the energy of polaron increases.