What Bohmian mechanic says about arrival times of 1D vacuum squeezed states

TL;DR

This paper uses Bohmian mechanics to analytically compute the arrival time distribution of a quantum particle in a 1D vacuum squeezed state, revealing differences from standard quantum predictions.

Contribution

It provides a closed-form analytical expression for arrival times in Bohmian mechanics for squeezed states, contrasting with standard quantum results.

Findings

Analytical arrival time distribution derived for 1D vacuum squeezed states.

Bohmian predictions differ from standard quantum mechanics.

Closed-form solutions facilitate comparison between interpretations.

Abstract

We calculate the time of arrival probability distribution of a quantum particle using the Bohmian formalism. The pilot-wave is given by the wave function of the one dimensional vacuum squeezed state but written in the Schr\"odinger representation. We made use of the unitary representation of the symplectic group in the Hilbert space $L^2(\mathbb{R})$. The solution to the Bohmian equations are analytical function thus allowing for a closed expression of the time of arrival distribution which differs from the counterparts in the standard quantum mechanics formulation.