"What is the empirical content of quantum mechanics? Or how does the wave function assigned to a relate to the results of measurements on the system? The well-known connection rule is the , which has been precisely tested by experiments. It says that a (projective) measurement of an A on a system with the wave function |ψ⟩ will randomly obtain one of the of A, and the probability of obtaining an eigenvalue ai is given by |⟨ai|ψ⟩|2, where |ai⟩ is the corresponding to the eigenvalue ai."
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Shan Gao (199 pages, 8 figures. Draft of book published in 2017 by Cambridge University Press; quote from p. 6) text at books.google.com
https://en.wikiquote.org/wiki/Wave_function
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