2005/10/12 by Eric A. Galapon, F. Delgado, F.S. Delgado +4
Engineering · Mathematics · Physics and Astronomy · #Arrival time #Asymptotic distribution #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Distribution (mathematics) #Eigenfunction #Eigenvalues and eigenvectors #Engineering #Geometry #Infinity #Limit (mathematics) #Limiting #Mathematical analysis #Mathematics #Particle in a box #Physics #Point (geometry) #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Quantum optics and atomic interactions #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1103/physreva.72.042107
Accepted for publication in Phys. Rev. A
arxiv created 2005/10/12 · openalex publication_date 2005/10/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time-of-arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time-of-arrival eigenfunctions is also numerically investigated and demonstrated that the eigenfunctions evolve to have point supports at the arrival point at their respective eigenvalues in the limit of arbitrarily large confining lengths, giving insight into the ideal physical content of the Kijowsky distribution.