Using T k ( a ) = exp ⁡ ⁡ ( − − i ℏ ℏ p k a ) from above with k = x , y and Taylor expansion we get: R ⁡ ⁡ ( z , d t ) = exp ⁡ ⁡ [ − − i ℏ ℏ ( x p y − − y p x ) d t ] = exp ⁡ ⁡ ( − − i ℏ ℏ L z d t ) = 1 − − i ℏ ℏ L z d t + ⋯ ⋯ with L z = x p y − − y p x the z -component of the angular momentum according to the classical cross product.