Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-06T23:47:23.884Z Has data issue: false hasContentIssue false
  • English
  • Français

Discrete–continuous and classical–quantum

Published online by Cambridge University Press:  01 April 2007

THIERRY PAUL
THIERRY PAUL*
Affiliation:
Départemant de Mathématiques et Applications, Ecole Normale Supérieure and CNRS, 45 rue d'Ulm, F – 75230 Paris Cedex 05
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 2 , April 2007 , pp. 177 - 183
Copyright
Copyright © Cambridge University Press 2007

References

Bohr, N. (1913) On the constitution of atoms and molecules. Philosophical Magazine 26 1–25.Google Scholar
Born, M. (1927) The mechanics of the atom, Ungar, New York.Google Scholar
Gutzwiller, M. (1971) Periodic orbits and classical quantization conditions. J. Math. Phys. 12 343–358.CrossRefGoogle Scholar
Halmos, P. (1949) Finite dimensional vector spaces, Princeton University Press.Google Scholar
Heisenberg, W. (1925) Matrix mechanik. Zeitscrift für Physik 33 879–893.CrossRefGoogle Scholar
von Neuman, J. (1996) Foundations of quantum mechanics, Princeton University Press.Google Scholar
Paul, T. (2006) On the status of perturbation theory. Mathematical Structures in Computer Science in this volume.Google Scholar
Paul, T. (2006) Recontruction and non-reconstruction of wave-packets (preprint).Google Scholar
Perrin, J. (1905) Les atomes, Paris Presses Universitaires de France.Google Scholar
Poincaré, H. (1987) Les méthodes nouvelles de la mécanique céleste, Blanchard, Paris.Google Scholar
Schrödinger, E. (1926) Quantisierung und eigenvalues. Ann. der Physics 79.Google Scholar
Stoler, D. and Yurke, B. (1986) Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. Phys. Rev. Letters 57 13.Google Scholar