The classical definition of angular momentum is L = r × × p . The quantum-mechanical counterparts of these objects share the same relationship: L = r × × p where r is the quantum position operator, p is the quantum momentum operator, × is cross product, and L is the orbital angular momentum operator. L (just like p and r) is a vector operator (a vector whose components are operators), i.e. L = ( L x , L y , L z ) where L x, L y, L z are three different quantum-mechanical operators.