Wigner functions on a lattice - art. no. 032114

The Wigner functions on the one-dimensional lattice are studied. Contrary t o the previous claim in literature, Wiener functions exist on the lattice w ith any number of sites, whether it is even or odd. There are infinitely ma ny solutions satisfying the conditions which reasonable Wigner functions sh ould respect. After presenting a heuristic method to obtain Wigner function s, we give the general form of the solutions. Quantum-mechanical expectatio n values in terms of Wigner functions are also discussed.