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Physics, 28.06.2019 10:00 salvadorperez26

Prove the following identities that we assumed to calculate [h, x] in [h, p] in class. (a) let a, b and c be arbitrary matrices (possibly infinite dimensional) then prove the following commutator identity: [ab, c] = a[b, c] + [a, c]b . (b) show that the position-momentum commutator [x, p] = i~ generalizes to [x n , p] = i~nxn−1 . (c) assume that f(x) has a convergent taylor expansion, then show that [f(x), p] = i~ df dx (x) .

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