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Titlebook: An Introduction to Hilbert Space and Quantum Logic; David W. Cohen Textbook 1989 Springer-Verlag New York Inc. 1989 Functionals.algebra.de

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发表于 2025-3-21 17:33:25 | 显示全部楼层 |阅读模式
期刊全称An Introduction to Hilbert Space and Quantum Logic
影响因子2023David W. Cohen
视频video
学科分类Problem Books in Mathematics
图书封面Titlebook: An Introduction to Hilbert Space and Quantum Logic;  David W. Cohen Textbook 1989 Springer-Verlag New York Inc. 1989 Functionals.algebra.de
影响因子Historically, nonclassical physics developed in three stages. First came a collection of .ad hoc. assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
Pindex Textbook 1989
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发表于 2025-3-21 21:43:12 | 显示全部楼层
Textbook 1989y strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
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https://doi.org/10.1007/978-3-642-65598-2 quantum mechanics. In Part B we outline a set of working hypotheses for quantum mechanics. In Part C we discuss a philosophical dilemma arising from these hypotheses and articulated in a famous paper written in 1935 by Einstein, Podolsky, and Rosen.
发表于 2025-3-22 16:32:42 | 显示全部楼层
0941-3502 ns known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Ins
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https://doi.org/10.1007/978-3-642-50181-4nts whose outcome sets are more general than the finite subsets of ℜ we saw in Chapter 1. We shall be guided by Lemma 1B.10, however, when we define the expected value of an observable as the integral of the identity function on ℜ with respect to a measure determined by a state on the logic.
发表于 2025-3-23 01:30:15 | 显示全部楼层
Subspaces in Hilbert Space,ing particle usually means obtaining an outcome from an infinite number of possibilities. In this chapter we shall learn about infinite dimensional Hilbert spaces. In particular, we shall consider the subspace structure of infinite dimensional Hilbert spaces. These provide the logics for orthodox quantum physics.
发表于 2025-3-23 09:00:34 | 显示全部楼层
,State Space and Gleason’s Theorem,nts whose outcome sets are more general than the finite subsets of ℜ we saw in Chapter 1. We shall be guided by Lemma 1B.10, however, when we define the expected value of an observable as the integral of the identity function on ℜ with respect to a measure determined by a state on the logic.
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