A unique one-body position operator for periodic systems
arXiv:2111.12538 · doi:10.1103/PhysRevB.105.235201
Abstract
In this work we proof that the one-body position operator for periodic systems that we have recently proposed [Phys. Rev. B 99, 205144] is unique modulo a phase factor and an additive constant. The proof uses several general physical constraints that a periodic one-body position operator should satisfy. We show that these constraints are sufficient to uniquely define a position operator that is compatible with periodic boundary conditions.
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