Probabilistic Parallels in the Classical Limit of Quantum Mechanical Models

2024/11/04 by Raghunathan Ramakrishnan, Ramakrishnan, Raghunathan
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2411.02329

openalex publication_date 2024/11/04 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28

Abstract

At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in the measurement of the particle's position. This resolution in the position can be related to the resolution of the secondary total angular momentum quantum number (m) when interpreting the probabilistic outcomes of the Stern--Gerlach-type thought experiments for large values of the angular momentum quantum numbers (j).

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