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8.1.5 Outcome of a single experiment

The outcome of a measurement of any quantity can only be the set of natural values of such a quantity. These are just the eigenvalues of $ \hat{O}$

$\displaystyle \hat{O}$fn(x) = onfn(x). (8.10)

Is this immediately obvious from the formalism? The short answer is no, but suppose we measure the value of the obervable for a wave function known to be an eigenstate. The outcome of a measurement better be this eigenvalue and nothing else. This leads us to surmise that this rule holds for any wave function, and we get the answer we are looking for. This also agrees with the experimentally observed quantisation of observables such as energy.



© 1998 Niels Walet, UMIST
Email Niels.Walet@umist.ac.uk