We have investigated the electronic structure of the conduction band states in InAs quantum boxes embedded in GaAs. Using cross-sectional scanning tunneling microscopy and spectroscopy, we report the direct observation of standing wave patterns in the boxes at room temperature. Electronic structure calculation of similar cleaved boxes allows the identification of the standing waves pattern as the probability density of the ground and first excited states. Their spatial distribution in the (001) plane is significantly affected by the strain relaxation due to the cleavage of the boxes.