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We present a numerically stable re-formulization of the transfer matrixmethod (TMM). The iteration form of the traditional TMM is transformed intosolving a set of linear equations. Our method gains the new ability ofcalculating accurate wave-functions of higher dimensional disordered systems.It also shows higher efficiency than the traditional TMM when treating finitesystems. In contrast to the diagonalization method, our method not onlyprovides a new route for calculating the wave-function corresponding to theboundary conditions of open systems in realistic transport experiments, butalso has advantages that the calculating wave energy/frequency can be tunedcontinuously and the efficiency is much higher. Our new method is further usedto identify the necklace state in the two dimensional disordered Andersonmodel, where it shows advantage in cooperating the wave-functions with thecontinuous transmission spectrum of open systems. The new formulization is verysimple to implement and can be readily generalized to various systems such asspin-orbit coupling systems or optical systems.

A re-formulization of the transfer matrix method for calculating wave-functions in higher dimensional disordered open systems