We can now readily calculate the commutator while calculating commutators of α α i matrixes and scaled L ~ ~ i and noticing that the symmetric Gaussian state e − − a r 2 is annihilating in average the terms containing mixed variable like x p y . Calculating 9 commutators (mixed may be zero by Gaussian example and the L z α α z = α α z L z = 0 since those matrices are counter-diagonal) and estimating terms from the norm of the resulting 4 × × 4 matrix containing four 2 3 factors giving square of the most natural L 2 , 1 norm of this matrix as 48 ≈ ≈ 49 = 7 2 ≈ ≈ 8 2 and using the norm inequality for the estimate