  In this paper, a new method based on Greens function theory and Fourier
transform analysis has been proposed for calculating band structure with high
accuracy and low processing time. This method utilizes sampling of potential
energy in some points of crystals unit cell with Dirac delta functions, then
through lattice Fourier transform gives us a simple and applicable formula for
most of nanostructures. Sampling of potential in a crystal lattice of any kind
contains accurate approximation of actual potential energy of atoms in the
crystal. The step forward regarding the method concentrated on two novel ideas,
Firstly, the potential was sampled and approximated by delta functions spread
over the unit cell. Secondly, the principal equation of lattice is translated
into reciprocal lattice and resulted in a huge reduction of calculations. By
this method, it is possible to extract the band structure of any one, two or
three dimensional crystalline structure.
