(a) Work out all of the canonical commutation relations for components of the operators r...

(a) Work out all of the canonical commutation relations for components of the operators r and p: [x, y], [x, py], [x, px], [py, pz], and so on. Answer:

 [4.10]

where the indices stand for x, y, or z, and rx = x, ry = y, and rz = z.

(b) Confirm Ehrenfest's theorem for 3-dimensions:

 [4.11]

(Each of these, of course, stands for three equations—one for each compo­nent.) Hint: First check that Equation 3.71 is valid in three dimensions.

(C) Formulate Heisenberg's uncertainty principle in three dimensions. Answer:

 [4.12]

but there is no restriction on, say,