The angular momentum is L_i = r_i x p_i.

This can also be written:

L_i = eps_ijk r_j p_k

L_i = -i hb (phi^ d/dtheta - theta^/sin(theta) d/dphi) = r r^ cross (hb/i del) in spherical coordinates.

Commutation relations:

1. [L_i,r]=[L_i,f(r)]=0
2. [L^2,H]=0 => angular momentum conserved

L_r = 0, L_theta = -p_phi/sin(theta) L_phi=p_theta

=> L^2=p_phi/sin^2(theta) + p_theta^2

L_i=-i hb eps_ijk(x_j d/dx_k-x_k d/dx_j) in Cartesian coordinates.

L_x= -i hb (sin(phi) d/dtheta + cos(phi)/tan(theta) d/dphi)

L_y= -i hb (-cos(phi) d/dtheta + sin(phi)/tan(theta) d/dphi)

L_z= -i hb d/dphi

L^2=- hb^2 (d/dtheta^2 + 1/tan(phi) d/dtheta + 1/ sin^2(theta) d/dtheta^2)