Detlef D\"urr, arrival-time distributions, and spin in Bohmian mechanics: Personal recollections and state-of-the-art

TL;DR

This paper discusses the arrival-time distributions in quantum mechanics, focusing on Bohmian particles and their experimental implications, especially for spin-polarized electrons in waveguides, highlighting recent research and personal recollections.

Contribution

It provides a selective examination of the arrival-time problem in quantum mechanics, emphasizing Bohmian distributions and recent experimental scenarios involving spin-polarized electrons.

Findings

Bohmian arrival-time distributions can be exotic and differ from classical expectations.

Recent studies show specific behaviors of spin-polarized electrons in waveguides.

The paper highlights the motivations and circumstances behind these theoretical developments.

Abstract

I recount here my association with Prof. Detlef D\"urr leading to our memorable research collaboration on arrival-time distributions in quantum mechanics. He influenced my life, both personally and professionally, as few others have or ever will. Detlef is my role model for what a brilliant, discerning scientist, academic, and mentor can and should be. The "arrival-time problem" in quantum mechanics is examined selectively, with an emphasis on the arrival-time distributions of Bohmian particles. In what follows, the "exotic" Bohmian arrival-time distributions of spin-polarized electrons accelerating down a cylindrical waveguide [S. Das and D. D\"urr, Sci. Rep. 9: 2242 (2019)], and some variations thereof are discussed. I shall not go into the mathematical treatment more than is necessary to spell out the key results. The intention is to document the circumstances and motivations underlying the ideas.