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Discrete–continuous and classical–quantum


We present a discussion concerning the opposition between discreteness and the continuum in quantum mechanics. In particular, it is shown that this duality was not restricted to the early days of the theory, but remains current, and features different aspects of discretisation. In particular, the discreteness of quantum mechanics is key for quantum information and quantum computation. We propose a conclusion involving a concept of completeness linking discreteness and the continuum.

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M. Gutzwiller (1971) Periodic orbits and classical quantization conditions. J. Math. Phys. 12 343358.

W. Heisenberg (1925) Matrix mechanik. Zeitscrift für Physik 33 879893.

N. Bohr (1913) On the constitution of atoms and molecules. Philosophical Magazine 26 125.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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