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The closed analytical expression for the electron density of states functionin a rectangular lattice is derived in an elementary way in terms of completeelliptic integrals of the first kind. The lattice can be treated as a deformedsquare lattice under uniform uniaxial stress (or strain). In contrast tohydrostatic case the uniaxial pressure, say along axis y, modifies a length ofthe y-bonds while the x-bonds remain intact. It also alters the correspondingtight-binding transfer integral gamma_2 between two y-nearest-neighboursleaving unchanged the gamma_1 for x-nn interactions. Due to stress-inducedlowering symmetry of this simple model one can get an insight into thedecoupling of its density of states on dependence of the lattice deformation ortransfer integrals anisotropy.

Density of electron states in a rectangular lattice under uniaxial stress