PACS 71.15.Dx, 71.15.Qe, 73.21.Fg We calculate the electron structure of δ-doped GaAs quantum wells within a realistic sp 3 s* tight-binding formalism, including spin. The results reveal the existence of a series of many quasi-bound states with a very strong spatial and energetic localization. For a donor impurity concentration of n 2D =1×10 13 cm -2 the full width at half maxima (FWHM) of the first quasi-bound state is 1.5×10-3 meV and the corresponding mean-life time is about 4 ns. This value is 10 3 times greater that the mean lifetime reported for Bragg's reflectors based on quantum wells. We find many similar features of the symmetry, spatial and energetic characteristics between quasi-bound and bound states.The study of the bound states in semiconductor quantum systems is very old and extensive. Nevertheless, the study of the quasi-bound states is a new one. The eigen-values change significantly from one system to another, but the shape of the eigen-functions is similar. The nature of the quasi-bound states can be different. There are quasi-bond states formed by the presence of two thin barriers [1, 2], a barrier [3,4], a quantum well with a finite superlattice [5] or only a quantum well [6]. Optical transitions between the conduction band states arising from spatial confinement in quantum Heteroestructuras have been observed for the first time by West and Eglash [7]. These transitions having enhanced intersubband oscillator strengths can be used for novel electronic and optical device applications. The technology of quantum well infrared photodetectors (QWIP's), an intersubband device, has progressed as a rapid pace since the demonstration of the first GaAs/AlGaAs QWIP, which employed a photo-excited tunnelling intersubband transition [8]. Voltage-tuneable multi-wavelength QWIP's [9] and QWIP's with narrow-band IR detection [10] have also demonstrated their advantages in the practical applications. Superlattice modulators exploiting the large linear Stark shift in intersubband transitions in quantum wells [11] and tunnellingelectron-assisted modulators [12] have been explored due to their potentially ultra-fast operation. Intersubband lasers emitters have been proposed and fabricated [13]. Quantum cascade electroluminiscent devices have been recently reported [14][15][16] The so called quasi-bound states appear in the continuum spectrum for some kind of potentials [17]. The existence of quasi-bound states has been reported in [18][19][20][21][22][23][24]. These states can be exploited in photo-detectors, modulators and switching devices.As we can see from the literature, the above barrier states are normally studied for rectangular potential profiles. In the present paper we study quasi-bound states in δ-doped GaAs quantum wells. The calculations are performed within the realistic sp 3 s * semi-empirical tight-binding model including spin.