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) .

answer would be letter choice (a),   a ball resting on a shelf. would be another example of potential energy   >   stored energy > not moving.

a ball spinning on a finger   >   kinetic energy > moving energy

a ball rolling on the ground   >   kinetic energy   > moving energy

a   ball flying through the air   > kinetic energy   >   moving energy

hope that                                         : )

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