Limiting distribution of periodic position measurements of a quantum harmonic oscillator

TL;DR

This paper analyzes the long-term behavior of position measurements in a quantum harmonic oscillator, showing that the measured positions converge to a specific limiting distribution as the number of measurements increases.

Contribution

It derives an explicit expression for the limiting distribution of position measurements and validates it through numerical simulations.

Findings

Measured positions converge to a limiting distribution

Derived explicit formula for the limiting distribution

Numerical simulations confirm theoretical predictions

Abstract

We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the number of measurements tends to infinity. We derive the expression for the limiting position distribution and validate it with numerical simulation.