Scheme for generalized maximally localized Wannier functions in one dimension

Maximally localized Wannier functions are the key tool for a variety of physical applications of Bloch states. Here we develop a simple and exact procedure to construct maximally localized Wannier functions for one dimensional periodic potentials of arbitrary form. As opposed to relatively complex numerical minimization approaches that may return somewhat different results depending on implementation and running conditions, this computationally straightforward method guarantees a unique (and optimal) result on each run. These features make it a useful vehicle for evaluation of Hubbard interactions, overlaps and various matrix elements in a simple and efficient manner.