The band model is applied to perfect crystals with translational symmetry, to find the electronic structure of the system. Following the work of Slater and Koster , the electronic wave functions are approximated by linear combinations of atomic orbitals, in term of Bloch sums, used as basis functions. Starting with an atomic orbital , located on an atom at , the Bloch sum is written as
Further simplifications are needed to calculate the integrals above. Slater and Koster  proposed to neglect the three-center integrals with respect to the two-center integrals. The three-center integrals involve two orbitals located at different atoms, and a potential part of the Hamiltonian due to a third atom. Thus, in the Slater and Koster's approach, only the potential (considered spherical) due to the two atoms upon which the orbitals are located, is taken into account. The integrals can therefore be replaced by parameters which depend on the internuclear distance , and on the symmetry of the orbitals involved. For example, if had the symmetry of a p orbital, it could be expressed as a linear combination of and , where and refer to the component of the angular momentum around the axis between the two atoms.
The Hamiltonian matrix elements can therefore be written