Quantum Mechanics - Commutation Relations

Let be a quantum mechanical angular momentum operator. The commutator [, ] is equivalent to which of the following?

A. 0
B. iħ
C. iħ
D. −iħ
E. iħ

(GR0877 #95)

Solution: 

Commutator identities: [A, B] = − [B, A]

and, [B, AC] = A[B, C] + [B, A]C 

[, ] = − [, ]

A = 
B = 
C = 

[, ] = [, ] +  [, ]
= [, ] + 0
= [iħ] + 0

− [, ] = −iħ

Answer: D