The group velocity v of the electron is given by v ( k ) = 1 ℏ ℏ d E d k , where E ( k ) denotes the dispersion relation for the given energy band. Suppose that the latter has the (tight-binding) form E ( k ) = A cos ⁡ ⁡ a k , where a is the lattice parameter and A is a constant. Then v ( k ) is given by v ( k ) = 1 ℏ ℏ d E d k = − − A a ℏ ℏ sin ⁡ ⁡ a k , and the electron position x can be computed as a function of time: x ( t ) = ∫ ∫ 0 t v ( k ( t ′ ) ) d t ′ = x ( 0 ) + A e E cos ⁡ ⁡ ( a e E ℏ ℏ t ) .