We present a numerically stable re-formulization of the transfer matrix method (TMM). The iteration form of the traditional TMM is transformed into solving a set of linear equations. Our method gains the new ability of calculating accurate wave-functions of higher dimensional disordered systems. It also shows higher efficiency than the traditional TMM when treating finite systems. In contrast to the diagonalization method, our method not only provides a new route for calculating the wave-function corresponding to the boundary conditions of open systems in realistic transport experiments, but also has advantages that the calculating wave energy/frequency can be tuned continuously and the efficiency is much higher. Our new method is further used to identify the necklace state in the two dimensional disordered Anderson model, where it shows advantage in cooperating the wave-functions with the continuous transmission spectrum of open systems. The new formulization is very simple to implement and can be readily generalized to various systems such as spin-orbit coupling systems or optical systems.

翻译：我们展示了转移矩阵法的数值稳定的重新成形方法。传统TMM的迭代形式被转化成解决一套线性方程式。我们的方法获得了计算高维无序系统精确波函数的新能力。在处理有限系统时,也显示出比传统的TMM更高的效率。与分解方法相反,我们的方法不仅为计算与现实运输实验中开放系统的边界条件相对应的波函数提供了一条新的路线,而且还具有以下优势:计算波能/频率可以不断调整,效率要高得多。我们的新方法还被用来进一步确定两个维无序安德森模型中的项链状态,这显示在与开放系统的连续传输频谱配合波函数方面有优势。新的形式化非常简单,可以实施,并且可以很容易地推广到各种系统,例如旋转轨道联动系统或光学系统。