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Canonical Quantization and Impenetrable Barriers
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Canonical Quantization and Impenetrable Barriers
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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).
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Cited by 1 Pith paper
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All Hilbert spaces are the same: consequences for generalized coordinates and momenta
All separable Hilbert spaces of given dimension being isomorphic implies exactly six basic generalized coordinate operators and seven coordinate-momentum pairs via self-adjoint or Neumark extensions.
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