Canonical Quantization and Impenetrable Barriers

DOI10.1119/1.1688784arXivmath-ph/0310023MaRDI QIDQ6469037

Piotr Garbaczewski, Waldemar Karwowski

Publication date: 14 October 2003

Abstract: We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by boundary conditions. By invoking an exemplary case of a particle in an infinite well, we analyze spectral problems for related, confined and global, observables. In particular, we show how one can make sense of various operators pertaining to trapped particles by not ignoring the rest of the real line (e.g., that space which is never occupied by the particle in question).

Mathematics Subject Classification ID

Mathematical logic and foundations (03-XX) Numerical analysis (65-XX)

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