By using matsubara green function theory , we have studied the magonon spectrum and calculated the magnon dispersion curve on the line in the brillouin zone for different parameters in the system 利用格林函数方法研究了磁振子声子相互作用下的二维绝缘铁磁体的磁振子谱，计算了布里渊区的线上的磁振子色散曲线。
The influences of longitudinal phonon and transverse phonon on the softening and broadening in the magnon linewidth are compared , and the influences of the parameters are also illustrated 比较了纵向声子与横向声子对磁振子谱的软化与磁振子谱线增宽的影响，也讨论了各项参数的变化对磁振子谱的软化与磁振子谱线增宽的影响。
Using the plane wave expansion method , from the computation result for the band gaps structure of infinitd periodic one dimension phononic crystal , it is found the width of the first gap relates with the material portion ratio 利用平面波展开法，计算一维无限周期结构声子晶体的带隙结构，发现每一带隙的宽度与材料的组份比有关。
Topics covered include crystal structure and band theory , density functional theory , a survey of properties of metals and semiconductors , quantum hall effect , phonons , electron phonon interaction and superconductivity 内容包括了晶体结构和能带理论，密度泛函理论，金属和半导体特性概论，量子霍尔效应，声子，电子-声子的相互作用以及超导电性。
In chapter three we study the properties of solitons in protein molecular systems by method of quantum coherent states , and obtained the improved temperature stability of the solitons due to the cubic nonlinear phonon potential 第三章利用量子相干态方法研究蛋白质分子链系统中孤立子特征，得到了考虑声子三阶非线性作用势下孤立子温度稳定性提高的结论。
In the forth chapter , we present the subsequent development of the renormalization group methods at the beginning . then based upon the electron - phonon model , we explain how to apply these methods to obtain the flow equations of the model 在第四章中首先介绍了重整化群方法的最新发展，并结合电子?声子模型详细介绍了如何用重整化群流方程方法导出系统的流方程。
