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"This gives some measure of how far oﬀ we would be likely to be from the expectation value for an average measurement. The general case for this can be derived. For an operator Q, then the wavefunction can be expressed as an expansion in eigenstates of Q " and writes the wavefunction as a sum over the eigenstates with coefficients whose modulus squared represent the probabilities of each eigenstate.

Could someone show me the derivation please?

Thanks!