The Quantum-Mechanical Position Operator in Extended Systems

Details The Quantum-Mechanical Position Operator in Extended Systems The Quantum-Mechanical Position Operator in Extended Systems

1997-09-27

arxiv.org/abs/cond-mat/9709306v1

Physics

Condensed Matter

Materials Science

Four pages in RevTeX

Scientific paper

10.1103/PhysRevLett.80.1800

The position operator (defined within the Schroedinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wavefunction, as usual in condensed matter physics. We show how to define the position expectation value by means of a simple many-body operator acting on the wavefunction of the extended system. The relationships of the present findings to the Berry-phase theory of polarization are discussed.

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