Wannier functions of elliptic one-gap potentials

Details Wannier functions of elliptic one-gap potentials Wannier functions of elliptic one-gap potentials

2004-01-22

arxiv.org/abs/cond-mat/0401440v2

Physics

Condensed Matter

Soft Condensed Matter

24 pages, 5 figures

Scientific paper

10.1088/0305-4470/37/41/007

Wannier functions of the one dimensional Schroedinger equation with elliptic one gap potentials are explicitly constructed. Properties of these functions are analytically and numerically investigated. In particular we derive an expression for the amplitude of the Wannier function in the origin, a power series expansion valid in the vicinity of the origin and an asymptotic expansion characterizing the decay of the Wannier function at large distances. Using these results we construct an approximate analytical expression of the Wannier function which is valid in the whole spatial domain and is in good agreement with numerical results.

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