In this problem you will derive the commutator a. The angular momentum vector in three...

In this problem you will derive the commutator

a. The angular momentum vector in three dimensions has the form l = i l_x + j l_y + kl_z where the unit vectors in the x, y, and z directions are denoted by i, j, and k . Determine l_x, l_y, and l_z by expanding the 3 × 3 cross product l = r × p. The vectors r and p are given by r = i_x + j _y + k_z and p = ip_x + jp_y +kp_z.

b. Substitute the operators for position and momentum in your expressions for l_x and l_y. Always write the position operator to the left of the momentum operator in a simple product of the two.

c. Show that