Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

TL;DR

This paper explores the relationship between quantum and classical trajectories in coherent states, demonstrating their equivalence in harmonic oscillators and analyzing their behavior in various potentials using a modified de Broglie-Bohm approach.

Contribution

It introduces a modified de Broglie-Bohm scheme that shows classical and quantum trajectories coincide for coherent states, extending the analysis to different potentials.

Findings

Quantum trajectories match classical ones in harmonic oscillators.

Almost identical trajectories are observed in infinite potential wells.

Periodic motion emerges in Poschl-Teller potential at large times.

Abstract

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories are those conceived in a modified de Broglie-Bohm scheme and we note that identical classical and quantum trajectories for coherent states are obtained only in the present approach. The study is extended to Gazeau-Klauder and SUSY quantum mechanics-based coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller (PT) potential by solving for the trajectories numerically. For the coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the PT potential, though classical trajectories are not regained, a periodic motion results as t --> \infty.