Multiphase semiclassical approximation of the one-dimensional harmonic crystal: I. The periodic case

Abstract. One-dimensional electronic conduction is investigated in a special case usually referred to as the harmonic crystal, meaning essentially that atoms are assumed to move like coupled harmonic oscillators within the Born–Oppenheimer approximation. We recall their dispersion relation and derive a WKB system approximately satisfied by any electron's wavefunction inside a given energy band. This is then numerically solved according to the method of K-branch solutions. Numerical results are presented in the case where atoms move with one- or two-modes vibrations; finally, we include the case where the Poisson self-interaction potential also influences the electrons' dynamics.