Question

One instance of this operation is set equal to “negative one times the interaction Hamiltonian” to transform a system into a dressed ground state in the Schrieffer–Wolff transformation. Hadamard’s lemma, which expresses “e-to-the-B times A times e-to-the-negative-B” in terms of a series of this operation, (15[1])is a special case (15[1])of the Baker–Campbell–Hausdorff (15[3]-5[1])formula. (15[3])The time evolution of operators in the (*) Heisenberg picture is given by an instance of this operation containing the Hamiltonian. (10[1])The expectation of “one over 2 i times an instance (10[1])of this operation” all squared appears in the generalized uncertainty principle. Two variables are canonically conjugate if applying this operation (10[1])to them yields “i times (-5[1])h-bar.” (10[2])For 10 points, name this operation that takes “A and B” and returns “A times B minus B times A.” (10[1])■END■

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