Postulate of the Averaged Measured Values

In the context in which the state function/(jc, y, z, t), in general a complex function, does not correspond to an eigen-function, the application of the operator 0 f does not produce the same measured value at reloading of the same experiment what is actually measured is not an eigen -value of the system, but an averaged measured value (x) y 

This averaged value, being also a number, it can be obtained from Eq. (3.1), since proceeding to the replacement multiplying to the 

Note how the space-time volume element dx is defined as the product between the elementary temporal variation dt and the spatial volume element dv=dxdydz, which for a system composed of N particles become 3N dimensional, so called the configuration space. 

by comparing the Eqs. (3.1) and (3.2), one observes how the averaged measured value (a) is identified with the eigen-value a if the condition according which the denominator from Eq. (3.2) is identical with the unity is satisfied, thus defining the normalization condition (Putz, 2006)  

In other words, the eigen-fimctions /which generate the eigen-values a 

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