Impenetrable barriers and canonical quantization

2003/10/31 by Piotr Garbaczewski, P. Garbaczewski, W. Karwowski · 2 citations
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #msc:03.65 #quant-ph

paper · pdf · doi:10.1119/1.1688784

published as Am. J. Phys. 72, (2004), 924-933 · to appear in Am.J.Phys (2004)

arxiv created 2004/02/04 · openalex publication_date 2004/06/14 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

We address an apparent conflict between the traditional canonical quantization framework of quantum theory and spatially restricted quantum dynamics when the translation invariance of an otherwise free quantum system is broken by boundary conditions. By considering the example of a particle in an infinite well, we analyze spectral problems for related confined and global observables. In particular, we show how we can interpret various operators related to trapped particles by not ignoring the rest of the real line that is never occupied by a particle.

Citations

• Fractional wave-function revivals in the infinite square well
• Visualizing the collapse and revival of wave packets in the infinite square well using expectation values
• Entropic uncertainty relations for the infinite well
• Mathematical surprises and Dirac's formalism in quantum mechanics

Cited by

• From a particle in a box to the uncertainty relation in a quantum dot and to reflecting walls for relativistic fermions
• Instantaneous Spreading Versus Space Localization for Nonrelativistic Quantum Systems