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I am trying to teach myself some quantum mechanics and here is something I am stuck on. Various derivations of Heisenberg uncertainty start out with two Hermitian operators, usually called A and B to represent position and momentum. Then they define another two operators ∆A and ∆B as:

∆A = A − < A > ∆B = B − < B >

That appears to me to say that ∆A equals operator A minus the expectation value of A. But how can you subtract a number from a matrix? Is an operator like a variable or is it more like a function? If it is like a function, then how can you plug ∆A and ∆B into the Cauchy-Schwartz inequality? This is probably a dumb question, but I don't think I can move on until I sort it out. Example of said derivation at:

"www.physics.ohio-state.edu/~jay/631/uncert1.pdf"[/URL]

Thanks for any help.

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# Heisenberg uncertainty derivation

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