Quantum-Mechanical Position Operator in Extended Systems

Raffaele Resta
Phys. Rev. Lett. 80, 1800 – Published 2 March 1998
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Abstract

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

  • Received 15 September 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.1800

©1998 American Physical Society

Authors & Affiliations

Raffaele Resta

  • INFM-Dipartimento di Fisica Teorica, Università di Trieste, Strada Costiera 11, 34014 Trieste, Italy
  • and Department of Physics, The Catholic University of America, Washington, D.C. 20064

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Vol. 80, Iss. 9 — 2 March 1998

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