Exercise 2: (a) Show that the generalised total angular momentum operators Ĵ₁ = Ĵ, (¹) + Ĵ(2) for a system of 2 particles with spin j₁, j2 respectively, satisfy the so(3) Lie algebra commutation relations 3 [Ji, j] = ikk k=1 (b) Prove that where [Ĵ², Ĵ]=0, = 3 i=1
Exercise 2: (a) Show that the generalised total angular momentum operators Ĵ₁ = Ĵ, (¹) + Ĵ(2) for a system of 2 particles with spin j₁, j2 respectively, satisfy the so(3) Lie algebra commutation relations 3 [Ji, j] = ikk k=1 (b) Prove that where [Ĵ², Ĵ]=0, = 3 i=1
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![Exercise 2:
(a) Show that the generalised total angular momentum operators Ĵ₁ = Ĵ, (¹) + Ĵ(2) for
a system of 2 particles with spin j₁, j2 respectively, satisfy the so(3) Lie algebra
commutation relations
3
[Ji, j] = ikk
k=1
(b) Prove that
where
[Ĵ², Ĵ]=0,
=
3
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2437b9d-e2ad-49ef-bf1e-5f1a1e22adaa%2F6a0cba27-663d-4622-9738-ad35e7f64ec1%2Fx5jpscq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 2:
(a) Show that the generalised total angular momentum operators Ĵ₁ = Ĵ, (¹) + Ĵ(2) for
a system of 2 particles with spin j₁, j2 respectively, satisfy the so(3) Lie algebra
commutation relations
3
[Ji, j] = ikk
k=1
(b) Prove that
where
[Ĵ², Ĵ]=0,
=
3
i=1
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