Classically, orbital angular momentum is given by L = r×p, where p is the linear momentum. To go from classical mechanics to quantum mechanics, replace p by the operator −i∇ (Section 15.6). Show that the quantum mechanical angular momentum 48 Chapter 1 Vector Analysis operator has Cartesian components (in units of ¯ h) Lx =− iy ∂ ∂z−z ∂ ∂y, Ly =− iz ∂ ∂x −x ∂ ∂z, Lz =− ix ∂ ∂y −y ∂ ∂x.

Question

Classically, orbital angular momentum is given by L = r×p, where p is the linear momentum. To go from classical mechanics to quantum mechanics, replace p by the operator −i∇ (Section 15.6). Show that the quantum mechanical angular momentum 48 Chapter 1 Vector Analysis operator has Cartesian components (in units of ¯ h) Lx =− iy ∂ ∂z−z ∂ ∂y, Ly =− iz ∂ ∂x −x ∂ ∂z, Lz =− ix ∂ ∂y −y ∂ ∂x.

anonymous · Answer

seems fairly straightforward if you know how cross product is defined