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Quantization Schemes for Euclidean Space

  • Brian C. Hall
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 267)

Abstract

One of the axioms of quantum mechanics states, “To each real-valued function f on the classical phase space there is associated a self-adjoint operator \(\hat{f}\) on the quantum Hilbert space.” The attentive reader will note that we have not, up to this point, given a general procedure for constructing \(\hat{f}\) from f.If we call \(\hat{f}\) the quantization of f,then we have only discussed the quantizations of a few very special classical observables, such as position, momentum, and energy.

Keywords

Poisson Bracket Momentum Operator Quantization Scheme Schmidt Operator Classical Phase Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Brian C. Hall
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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