Irreversible Behaviour and Collapse of Wave Packets in a Quantum System with Point Interactions

TL;DR

This paper analyzes how strong point interactions in a quantum system cause wave packet collapse and energy divergence, providing a model for quantum measurement and wave function collapse.

Contribution

It reveals the dynamical mechanism behind wave packet collapse and energy divergence in a coupled particle-oscillator system with point interactions.

Findings

Oscillator energy diverges exponentially over time.

Particle's spatial distribution collapses into a delta function.

Model suggests a formal framework for wave packet collapse during measurement.

Abstract

A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction. Here the simple dynamical mechanism underlying this phenomenon is exposed. The energy of the oscillator is proven to exponentially diverge in time, while the spatial probability distribution of the particle collapses into a delta function in the interaction point. On account of this result, a generalized model with many oscillators which interact with the particle at different points is argued to provide a formal model for approximate measurement of position, and collapse of wave packets.