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A quantum observable is a measurable operator whose corresponding property of the state can be determined by some sequence of physical operations ("observation"), such as submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states.

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Canonical momentum not observable vs energy is observable

I have seen explanations that canonical momentum for charged particles $p = mv + qA/c$ is not a measurable quantity/observable because it is not gauge invariant. However, there are many quantities tha …
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