  A new method for calculation of band structure has been proposed based on the
Green's function theory and local sampling. Potential energy in the Hamiltonian
of Schrodinger's equation is approximated with a series of sampled Dirac delta
functions weighted by appropriate factors. These factors are found from
multipole expansion of atomic potentials in the crystal lattice, with
considering effects such as screening. Fourier transform was then applied to
describe the wave function in reciprocal space. Sampling can be uniform or
non-uniform throughout space; however rate and interval optimization is
essential. Theory was implemented for Silicon, Germanium and Graphene sheet
individually, while results were compared with the ab-initio non-local
pseudopotential (AINLPS) method. Also for Silicon, the pseudopotential used in
orbital-free density functional theory (OF-DFT) was employed as a suitable
sampling source. Phase variations of the dispersion formula are analyzed,
introducing adapting parameters to improve compatibility with ab-initio
results. Local analysis with low order truncation in real space, reduces
implementation time while giving acceptable results.
