The #Heisenberg equation for the time evolution of an observable can be derived from this mix of #calculus and matrix/linear #algebra. #physics #mathpic.twitter.com/QYGOigWFUH
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Thank you, glad you like it. Sometimes I’ve wondered what matrix versions of some known limits would look like.
so the Heisenberg EOM would essentially amount to the LHS being equal to dA/dt.. so I imagine the way to show that would be expanding the exponents in a series?
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Yes, by just using the exponential series for the expression A exp(tB) - exp(tB) A (since exp(-tB) can be factored out and it goes to the identity as t goes to 0).
Thanks. Twitter will use this to make your timeline better. UndoUndo
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The BCH expansion might be a (sledgehammer) way of showing this, but it can also be proved using the product rulepic.twitter.com/8u7MUbuP3g
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Brian C. Hall. Lie Groups, Lie Algrbras and Representations.
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