the above equations, one need only consider external fields, while attempting the calculation from a set of equations of motion based on true momentum would require taking into account individual Coulomb and Lorentz forces of every single lattice ion in addition to the external field. Applications Angle-resolved photo-emission spectroscopy (ARPES) In angle-resolved photo-emission spectroscopy (ARPES), irradiating light on a crystal sample results in the ejection of an electron away from the crystal. Throughout the course of the interaction, one is allowed to conflate the two concepts of crystal and true momentum and thereby gain direct knowledge of a crystal's band structure. That is to say, an electron's crystal momentum inside the crystal becomes its true momentum after it leaves, and the true momentum may be subsequently inferred from the equation by measuring the angle and kinetic energy at which the electron exits the crystal, where is a single electron's mass. Because crystal symmetry in the direction normal to the crystal surface is lost at the crystal boundary, crystal momentum in this direction is not conserved. Consequently, the only directions in which useful ARPES data can be gleaned are directions parallel to the crystal surface. References Electronic band structures Moment (physics) Momentum