A comprehensive study of the velocity, momentum and position matrix elements for Bloch states using a local orbital basis

J. J. Esteve-Paredes, J. J. Palacios

We present a comprehensive study of the velocity operator, $\hat{\mathbf{v}}=\frac{i}{\hslash }[\hat{H},\hat{\mathbf{r}}]$, when used in crystalline solids calculations. The…