We present numerical calculations that support the existence of electronic states confined in the continuous part of the spectrum in single rectangular quantum wells and barriers. We study the conditions necessary for the creation of these states. We find strong energetic and spatial localization of quasi-bound states at high energies in the conduction band. The results can be used in the design of optoelectronic devices that operate on the basis of continuum bound states.

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The total density of states in rectangular AlGaAs/GaAs quantum wells are calculated numerically summing in the two-dimensional Brillouin zone. The quasi-two-dimensional energy bands are observed for typical wells and the integrated spectral strengths are presented. The conditions for the formation of quantum wells for all electron K-vectors are discussed.