The Hilbert Space Axiom in Quantum Mechanics

  • Stanley P. Gudder


The Hilbert space axiom is the basic postulate of conventional quantum mechanics. In essence it maintains that the observables for an isolated quantum mechanical system S can be represented by self-adjoint operators on a complex Hilbert space H; the states for S can be represented by density operators on H; and the dynamics can be represented by a one-parameter unitary group on H. The power of this axiom is indisputable, but what is its justification? Where does the Hilbert space come from? And if it is necessary to use Hilbert spaces, why must they be complex?


Quantum Mechanics Hide Variable Division Ring Definite Function Complex Hilbert Space 
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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Stanley P. Gudder
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of DenverDenverUSA

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