This interesting phenomenon manifests itself when spatial dimensions of the studied system become comparable to the corresponding (temperature-dependent, in general) de Broglie wavelength. In particular, confinement of carriers in a quantum dot (quantum confinement) will transform the continuous optical spectrum of a bulk semiconductor into a discrete one, leading, in turn, to experimentally observable cascades of discrete electronic transitions.
See the attached PhD thesis for more details and profound discussion of this issue.