Probability and Operators in Quantum Mechanics

  • Robert D. Richtmyer
Part of the Texts and Monographs in Physics book series (TMP)


This chapter contains a discussion of the role played by probability in the foundations of quantum mechanics and an introduction to the role it plays in quantum statistical mechanics.


States of a system observables measurement probabilistic axioms for a quantum mechanical system spectral projectors orthogonality of the projectors as a consequence of the probabilistic axioms cumulative probability for an observable probability basis for representation of an observable as a self-adjoint operator expectation variance uncertainty quantum mechanical ensemble the density matrix—a positive definite operator of unit trace expectation function expression of unbounded observables in terms of bounded ones commutation relations Banach algebra C*- and B*-algebras representation of B*- by C*-algebras positive definite element positive functional observable with a simple spectrum generating vector spectral representations of a Hilbert space complete set of commuting observables unitary “observables.” 


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Copyright information

© Springer-Verlag New York Inc. 1978

Authors and Affiliations

  • Robert D. Richtmyer
    • 1
  1. 1.Department of Physics and AstrophysicsUniversity of ColoradoBoulderUSA

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