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Mathematical Foundations of Quantum MechanicsNew Edition$
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John von Neumann

Print publication date: 2018

Print ISBN-13: 9780691178561

Published to Princeton Scholarship Online: September 2018

DOI: 10.23943/princeton/9780691178561.001.0001

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Deductive Development of the Theory

Deductive Development of the Theory

(p.193) Chapter IV Deductive Development of the Theory
Mathematical Foundations of Quantum Mechanics

John von Neumann

, Robert T. Beyer, Nicholas A. Wheeler
Princeton University Press

This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ‎] (∥φ‎∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ‎] is the state φ‎).

Keywords:   statistical theory, statistical formulas, statistical ensemble, states, deductive development

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