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proof of uncertainity principle without using braket vectors


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I don't think so as the general uncertainty principle depends on the states and in particular the commutator of the operators involved, roughly we have

 

[math] \langle \psi | [A,B] |\psi \rangle [/math].

 

It is because the commutator for the position and momentum is ~ i (in nice units) that the uncertainty principle does not depend on the states.

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