Density of electron states in a rectangular lattice under uniaxial   stress
  The closed analytical expression for the electron density of states function in a rectangular lattice is derived in an elementary way in terms of complete elliptic integrals of the first kind. The lattice can be treated as a deformed square lattice under uniform uniaxial stress (or strain). In contrast to hydrostatic case the uniaxial pressure, say along axis y, modifies a length of the y-bonds while the x-bonds remain intact. It also alters the corresponding tight-binding transfer integral gamma_2 between two y-nearest-neighbours leaving unchanged the gamma_1 for x-nn interactions. Due to stress-induced lowering symmetry of this simple model one can get an insight into the decoupling of its density of states on dependence of the lattice deformation or transfer integrals anisotropy. 
Ryszard Piasecki