Operational Definition
Quantum physics shows an inherent statistical behaviour: The measured outcome of an experiment will generally not be the same if the experiment is repeated several times. Only the statistical mean of the measured values, averaged over a large number of runs of the experiment, is a repeatable quantity. Quantum theory does not, in fact, predict the result of individual measurements, but only their statistical mean. This predicted mean value is called the expectation value.
While the computation of the mean value of experimental results is very much the same as in classical statistics, its mathematical representation in the formalism of quantum theory differs significantly from classical measure theory.
Read more about this topic: Expectation Value (quantum Mechanics)
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