DIRAC-LIKE BEHAVIOR OF A NONRELATIVISTIC TIGHT-BINDING HAMILTONIAN IN ONE DIMENSION

We study a linear periodic chain using opposite-parity wave-functions, localized in alternative sites, as a tight-binding LCAO basis. In the first nearest-neighbour approximation and in the continuum limit, we show that the 1-dimensional equation for the quantum amplitudes becomes Dirac-like. We study the electron-hole dynamics in this "relativistic" framework. We discuss in particular the "zitterbewegung" and the limit of vanishing "rest mass". © 1990.