In the consideration of the addition of angular momentums hat (^) = hat (^) ₁ + hat (^), prove that [hat (^)², hat()}] | = 0 = [hat(1)², hat(ɲ)²] but [hat(1)², hat ₁] 0 [hat (1), hat()2].
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![In the consideration of the addition of angular momentums hat (^) = hat (^) ₁ + hat (^), prove that [hat (^)², hat()}] | = 0 = [hat(1)², hat(ɲ)²] but [hat(1)², hat
₁] 0 [hat (1), hat()2].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90670015-b17c-4113-9f77-792fbd0d356d%2F80f22faa-a2e7-425e-abaa-2571e64a6f8a%2F7h4gp68_processed.jpeg&w=3840&q=75)
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- Please obtain the same result as in the book.Provide a written answerWe have a three dimensional vector space where |P1), |P2) and |23) form a complete orthonormal basis. In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5 i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|. ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".