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

Commutator identities: [A, B] = − [B, A]
and, [B, AC] = A[B, C] + [B, A]C
[
,
] = − [
, 
]
A =
B =
C =
[
, 
] =
[
,
] + [
,
]
=
[
,
] + 0
=
[iħ
] + 0
− [
, 
] = −iħ

Answer: D
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 =
[
=
=
− [
Answer: D
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