The Zeno Paradox in Quantum Mechanics

Abstract

The Quantum Zeno Effect slows the evolution of a quantum system through frequent measurements, preventing state transitions. In the limit of infinitely fast measurements, the evolution effectively freezes. Quantum Zeno Dynamics (QZD) extends this by confining the system to a subspace of its Hilbert space. This work examines QZD through position and momentum measurements modeled as Von Neumann projections. Frequent measurements confine the system within the projection subspace, leading to remarkable effects near its boundaries. Position measurements on a free particle induce momentum reversals, whereas momentum measurements on a particle in a symmetric potential give rise to the novel phenomenon of equipotential translocation.