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This paper presents theoretical calculations of the energy and wave function of the ground state and the first excited state of an electron confined in a GaAsAl/GaAs quantum well with a Morse potential profile using the effective mass approximation method and the envelope wave function. The intersubband transitions are analyzed according to the parameters that define the geometry of the Morse potential to represent the interdiffusion between materials of the barrier and the well. In addition, the peaks of the nonlinear optical rectification are shown as a function of energy of incident photons and their resonance with the transition energy between the two states. An electric field in the growth direction of the quantum well and a magnetic field perpendicular to the heterostructure are applied in order to study the shifts in the optical response peaks in the spectrum of the incident photons.