Band structure calculations take advantage of the periodic nature of a crystal lattice, exploiting its symmetry. The single-electron Schrödinger equation is solved for an electron in a lattice-periodic potential, giving Bloch electrons as solutions
where  is called the wavevector. For each value of , there are multiple solutions to the Schrödinger equation labelled by , the band index, which simply numbers the energy bands.
Each of these energy levels evolves smoothly with changes in , forming a smooth band of states. For each band we can define a function , which is the dispersion relation for electrons in that band.
The wavevector takes on any value inside the Brillouin zone, which is a polyhedron in wavevector (reciprocal lattice) space that is related to the crystal's lattice.
Wavevectors outside the Brillouin zone simply correspond to states that are physically identical to those states within the Brillouin zone.
Special high symmetry points/lines in the Brillouin zone are assigned labels like Γ, Δ, Λ, Σ (see Fig 1).
It is difficult to visualize the shape of a band as a function of wavevector, as it would require a plot in four-dimensional space,  vs. , , . In scientific literature it is common to see band structure plots which show the values of  for values of  along straight lines connecting symmetry points, often labelled Δ, Λ, Σ, or [[Miller index|[100], [111], and [110]]], respectively. Another method for visualizing band structure is to plot a constant-energy isosurface in wavevector space, showing all of the states with energy equal to a particular value. The isosurface of states with energy equal to the Fermi level is known as the Fermi surface.
Energy band gaps can be classified using the wavevectors of the states surrounding the band gap:
* Direct band gap: the lowest-energy state above the band gap has the same  as the highest-energy state beneath the band gap.
* Indirect band gap: the closest states above and beneath the band gap do not have the same  value.