Group theoretic formulation of complementarity

Understand

We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems.

• We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability density is displaced by spatial translations.
• In contrast a wave-like state is represented by a spatially-delocalized wave function and the corresponding broad position probability density is invariant to spatial translations.
• The wave-particle dichotomy can therefore be seen as a competition between displacement and invariance of the state with respect to spatial translations.