Quantization Schemes for Euclidean Space

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


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.


Poisson Bracket Momentum Operator Quantization Scheme Schmidt Operator Classical Phase Space 
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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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