How can expectation of position^2 be > L

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SUMMARY

The expectation of position squared, denoted as , can exceed the length of a box, represented as L, due to the dimensional differences between squared units and linear units. In the example provided, with L set to 100m, the calculation yields = 333m, illustrating that the square of a length (in square meters) is fundamentally different from the length itself (in meters). This discrepancy arises because while 100^2 is indeed greater than 100, the units of measurement must be considered, as square meters cannot be directly compared to meters.

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How can position^2 expectation be greater than the Length of "box"? I mean <x^2> = L^2 / 3. Say L=100m then we have <x^2> = 333m. How is this possible?
 
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Why should it not be possible? After all, ##100^2>100##. In any case the square is not comparable to the length, as the units of one is square metres and of the other is only metres. The volume of a cube that is 10cm per side is more than 10 ##cm^3##.
 

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