- #1

- 324

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What is the link between noncommuting observables

[tex]{\displaystyle [{\hat {A}},{\hat {B}}]={\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}} \neq 0}[/tex]

and indeterminacy principle (which is about inequality relation of standard deviation of the expectation value of observables A and B ) ?

If the observables commute we can find a complete set of simultaneous eigenvectors if not this implies that no quantum state can simultaneously be both A and B eigenstate. Why this implies that we cannot measure one without affecting statisticaly the other (uncertainty principle) ?

Is it possible to measure simultaneously the two incompatibles observables knowing that when a state is measured, it is projected onto an eigenstate in the basis of the relevant observable ?

best regards

Patrick