On Repeated Measurements of a Quantum Particle in a Harmonic Potential
Abstract
We study evolution of a quantum particle in a harmonic potential whose position and momentum are repeatedly monitored. A back-action of measuring devices is accounted for. Our model utilizes a generalized measurement corresponding to the Positive Operator-Valued Measure. We assume that upon measurement the particle's wavefunction is projected onto one of possible detector states depending on the observed result. We chose these post-measurement states to be moving Gaussian wavepackets. The Wave Function Quantum Monte-Carlo formalism is used to simulate single quantum trajectories of the particle. We show how classical trajectories emerge in course of observation and study in detail dispersion of position and momentum of the particle.
Keywords
Cite
@article{arxiv.2306.08342,
title = {On Repeated Measurements of a Quantum Particle in a Harmonic Potential},
author = {Filip Gampel and Mariusz Gajda},
journal= {arXiv preprint arXiv:2306.08342},
year = {2023}
}
Comments
This article belongs to the special issue of Acta Physica Polonica A printed in honor of Professor Iwo Bialynicki-Birula on the occasion of his 90th birthday (Ed. Tomasz Sowinski, DOI:10.12693/APhysPolA.143.S0)