The most probable wave function of a single free moving particle

TL;DR

This paper derives the most probable wave functions for a free quantum particle by maximizing Shannon entropy, revealing self-trapped solutions with finite support that move uniformly without changing shape.

Contribution

It introduces a novel approach to find the most probable wave functions for free particles using entropy maximization, uncovering self-trapped, shape-preserving solutions.

Findings

Identifies wave functions with finite spatial support that are self-trapped.

Shows these solutions move uniformly while maintaining their form.

Provides a new perspective on free particle quantum states.

Abstract

We develop the most probable wave functions for a single free quantum particle given its momentum and energy by imposing its quantum probability density to maximize Shannon information entropy. We show that there is a class of solutions in which the quantum probability density is self-trapped with finite-size spatial support, uniformly moving hence keeping its form unchanged.