薛定谔算子的迁移率边是分离绝对连续谱和纯点谱的临界能量，是凝聚态物理中非常重要的概念。物理上一般通过数值法研究迁移率边；数学上对迁移率边的研究比较少，大多集中在混合谱的讨论上。GAA模型和Mosaic模型是仅有的被严格证明存在精确迁移率边的两类模型。本文结合二者的特点推广了GAA模型和Mosaic模型，研究了一类新的具有精确迁移率边的一维离散拟周期模型。 本文研究了该一维离散拟周期薛定谔算子，应用全局理论明确求出了李雅普诺夫指数，求出了绝对连续谱的范围以及Anderson 局域的范围，并给出迁移率边的表达式。同时，严格证明了丢番图频率下，对几乎所有的相，满足不等式$|(\tau E+2\lambda )a_{\kappa}-2\tau a_{\kappa-1}| >2$ 的谱点都是Anderson局域的，即具有指数衰减特征函数的纯点谱；对所有的相，满足不等式$|(\tau E+2\lambda )a_{\kappa}-2\tau a_{\kappa-1}| <2$的谱点都是绝对连续谱。

The mobility edge of Schr\"{o}dinger operators is the critical energy for separating absolutely continuous spectrum and purely point spectrum, and is a very important concept in condensed matter physics. In physics, mobility edges are generally studied by numerical methods; In mathematics, the study of mobility edges is relatively rare, and most of them focus on the study of mixed spectra. GAA model and Mosaic model are the only two types of models that have been strictly proven to have exact mobility edges. In this thesis, we generalize the GAA model and Mosaic model based on their characteristics, study a new class of one-dimensional discrete quasi-periodic models with exact mobility edges, and give the expression of mobility edges. It is strictly proved that ,as for almost all phases with Diophantine frequency,the spectral points that satisfy the inequality $|(\tau E+2\lambda )a_{\kappa}-2\tau a_{\kappa-1}| >2$ are all Anderson localized. In other word,they are the purely point spectra with exponential decay characteristic functions. For all phases, the spectral points that satisfy the inequality $|(\tau E+2\lambda )a_{\kappa}-2\tau a_{\kappa-1}| <2$ are absolutely continuous spectra.