  The analogy between electromagnetic waves and ballistic electrons within the
Kane's model is developed and subsequently applied to a theoretical description
of a quantum version of a metamaterial planar lens. Restrictions imposed on the
perfect lens and the poor man's lens by available semiconductor band structures
are discussed. A realistic implementation is proposed for the quantum poor
man's lens, which uses specific properties of the HgTe compound. The properties
of the lens are presented on the basis of a calculated transmission of oblique
electrons through the lens structure.
