Say you have some operator A with an incomplete set of eigenstates, but the state of the system is such that it happens to be expressible as a sum (possibly infinite, or integral, whatever) of the eigenstates of A, and lets say the eigenvalues are real and whatever is necessary....we may assume that A is a dynamical variable. Can A be measured?(adsbygoogle = window.adsbygoogle || []).push({});

The justification that an observable must have complete eigenstates is that if you make a measurement corresponding to the observable on a system, the system will jump into one of the observables eigenstates. But why must any state be expressible as a sum of an operators eigenstates, rather than just the current one?

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# Homework Help: Can an operator without complete eigenstates be measured?

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