Is there any proof of the uncertainity principle without the use of braket vectors? If so please send me where to find it.

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.

hmm. i am thinking of how i could join these discussions...