A formalism of transfer matrix method is presented and used to solve a one-dimensional time-independent Schrdinger equation based on a simple one-band effective mass model and the envelope function approximation. The accuracy of this method is proved by comparing the numerical solution and analytical solution for a GaAs-based type Ⅰ single quantum well system， and its applicability is demonstrated by experimental photoluminescence results of the InAs/GaSb-based type Ⅱ and broken-gap quantum well structures. The formalism is extended to calculating the subband energies and corresponding wavefunctions in the GaAs/GaAlAs-based type Ⅰ coupled multiple quantum well systems, showing that the formalism is universal and practical.