Bohmian quantum trajectories from coherent states

TL;DR

This paper demonstrates that Bohmian quantum trajectories derived from coherent states closely resemble classical trajectories, with exact agreement in complex cases and conjectured solutions in real cases, influenced by the Mandel parameter.

Contribution

It introduces a detailed analysis of Bohmian trajectories from coherent states, revealing their classical-like behavior and providing conjectures for analytical solutions.

Findings

Quantum potential is constant in complex cases, leading to exact agreement.

Trajectories are governed by the Mandel parameter, affecting wavefunction evolution.

Explicit demonstrations for harmonic oscillator and Pöschl-Teller potential.

Abstract

We find that real and complex Bohmian quantum trajectories resulting from well-localized Klauder coherent states in the quasi-Poissonian regime possess qualitatively the same type of trajectories as those obtained from a purely classical analysis of the corresponding Hamilton-Jacobi equation. In the complex cases treated the quantum potential results to a constant, such that the agreement is exact. For the real cases we provide conjectures for analytical solutions for the trajectories as well as the corresponding quantum potentials. The overall qualitative behaviour is governed by the Mandel parameter determining the regime in which the wavefunctions evolve as soliton like structures. We demonstrate these features explicitly for the harmonic oscillator and the Poeschl-Teller potential.