Motion of 'hopping' particles in a constant force field

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Abstract
The authors study the eigenstates of electrons or holes constrained to 'hop' from site to neighbouring site on a lattice ('Wannier particles'), when they are subjected to strong fields of constant force. Principal applications are to inversion layers at the surface of semiconductors. It is seen that the exact solutions differ considerably from those found in the continuum 'effective-mass' approximation. The authors also analyse the eigenstates of two Wannier particles when the only force is their mutual attraction of constant force.

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