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nomadreid

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- Eigenvalues of an observable are probability amplitudes but also stated to be measurement values. What am I missing?

This is a very elementary question, from the beginnings of quantum mechanics.

For simplicity, I refer to a finite case with pure states.

If I understand correctly, the spectrum of an observable is the collection of eigenvalues formed by the inner product of states and hence equal to probability amplitudes; they are then associated to the possible values of a measurement.

Hence I am confused by statements such as the following

“Eigenvalues of observables are real and in fact are possible

How can the square roots of probabilities, which are less than one, be values of measurements (which can be greater than one)?

For simplicity, I refer to a finite case with pure states.

If I understand correctly, the spectrum of an observable is the collection of eigenvalues formed by the inner product of states and hence equal to probability amplitudes; they are then associated to the possible values of a measurement.

Hence I am confused by statements such as the following

“Eigenvalues of observables are real and in fact are possible

*outcomes*of*measurements*of a given*observable*.” (https://www.quantiki.org/wiki/observables-and-measurements, but not the only example.)How can the square roots of probabilities, which are less than one, be values of measurements (which can be greater than one)?