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A complete quantum mechanical model for GaAs/AlGaAs quantum well infrared photodetectors(QWIPs) is presented here. The model consisted of four parts: (1) Starting with the description of the electromagnetic field of the infrared radiation in the QWIP, effective component of the vector potential 〈|Az|〉 along the QWIP growth direction (z-axis) due to the optical diffraction grating was calculated. (2) From the wave transmissions and the occupations of the electronic states, it was discussed that the dark current in the QWIP is determined by the drift-diffusion current of carriers thermally excited from the ground sublevel in the quantum well to extended states above the barrier. (3) The photocurrent was investigated by the optical transition (absorption coefficient between the ground state to excited states due to the nonzero-〈|Az|〉 ). (4) By studying the inter-diffusion of the Al atoms across the GaAs/AlGaAs heterointerfaces,the mobility of the drift-diffusion carriers in the excited states was calculated, so the measurement results of the dark current and photocurrent spectra can be explained theoretically. With the complete quantum mechanical descriptions of (1-4), QWIP device design and optimization are possible.