The quantum-mechanical position operator and the polarization problem

Details The quantum-mechanical position operator and the polarization problem The quantum-mechanical position operator and the polarization problem

1998-01-31

arxiv.org/abs/cond-mat/9802004v1

Physics

Condensed Matter

Materials Science

10 pages, 1 embedded figure (in two panels). Presented at the Fifth Williamsburg Workshop on First-Principles Calculations for

Scientific paper

10.1063/1.56271

The position operator (defined within Schroedinger representation as usual) becomes meaningless when the usual Born-von Karman periodic boundary conditions are adopted: this fact is at the root of the polarization problem. I show how to define the position expectation value by means of rather peculiar many-body (multiplicative) operator acting on the wavefunction of the extended system. This definition can be regarded as the generalization of a precursor work, apparently unrelated to the polarization problem. For uncorrelated electrons, the present finding coincides with the so-called "single-point Berry phase" formula, which can hardly be regarded as the approximation of a continuum integral, and is computationally very useful for disordered systems. Simulations which are based on this concept are being performed by several groups.

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