1. The problem statement, all variables and given/known data from the cartesian definition of angular momentum, derive the operator for the z component in polar coordinates L_z = -ih[x(d/dy) - y(d/dx)] to L_z = -ih(d/dθ) 2. Relevant equations x = rcosθ y = rsinθ r^2 = x^2 + y^2 r = (x^2 + y^2)^1/2 3. The attempt at a solution first of all I'm not sure how this is even possible. Every derivation of the angular momentum operator I've seen requires spherical coordinates, not polar. I tried taking the derivative of r with respect to x to get cosθ and with respect to y to get sinθ and dx/dθ = -rsinθ dy/dθ = rcosθ but it's not getting me anywhere. is there something i should be rewriting d/dx and d/dy as?