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Feb 4, 2002 · 1. Quantum Mechanics as a Probability Calculus. It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the “quantum logic” of projection operators on a Hilbert space. []
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Supplement to Quantum Logic and Probability Theory. The...
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Oct 8, 2007 · To summarize, quantum probability is the most natural non-commutative generalization of classical probability. In this author’sopinion, this description does the most to demystify quantum probability and quantum mechanics. 1.1. Quantum superpositions We will begin by discussing part of the pure-state model of quantum mechanics in order to ...
nate definition of quantum mechanics; we will de-scribe it as a special case of pure-state matrix me-chanics. Since classical probability is a major analogy for us, it is reviewed in Section 1.10. In short, we can think of classical probability as a category Prob whose objects are measure spaces (or in the finite
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Is quantum mechanics a generalization of classical probability?
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In this chapter it is discussed from the perspective of whether and in what sense quantum mechanics requires a generalization of the usual (Kolmogorovian) concept of probability. The focus is on the case of finite-dimensional quantum mechanics (which is analogous to that of discrete probability spaces), partly for simplicity and partly for ease ...
The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as a semi-classical approximation to modern quantum mechanics.
For a classical mechanical system the sample space 92 is the classical phase space I' and the classical observable being real-valued functions on r, are the random variables. Therefore classical physics can be embedded in the classical probability calculus. If a theory however should be applicable to quantum physics we are
Mar 17, 2020 · There is a remarkable difference between classical probability and quantum probability when one considers two (or more) observables. In the case of classical probability there always exists one sample space \ ( \Omega \) together with its probability measure P, which describes any given probabilistic situation.
