making it safe to replace them with a fixed potential structure, and the macroscopic dimensions of a crystal are typically far greater than a single lattice spacing, making edge effects negligible. A consequence of this potential energy function is that it is possible to shift the initial position of an electron by any lattice vector formula_6 without changing any aspect of the problem, thereby defining a discrete symmetry. Technically, an infinite periodic potential implies that the lattice translation operator formula_8 commutes with the Hamiltonian, assuming a simple kinetic-plus-potential form.