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Jules Lamers
Jules Lamers
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  1. You're missing some terms in the third equality: the sum disappeared and you've dropped the terms where you take the commutators with the second spin operator in each product.

  2. a) That's correct. b) The result is nonzero if $l+1=n$. Hint: first work out the commutators between $S^+_i, S^-_j, S^z_k$ and then do the computation more carefully. c) WhatHint: what is the eigenvalue of $S^z_i$ on $\vert \Omega\rangle$?

  1. You're missing some terms in the third equality: the sum disappeared and you've dropped the terms where you take the commutators with the second spin operator in each product.

  2. a) That's correct. b) The result is nonzero if $l+1=n$. Hint: first work out the commutators between $S^+_i, S^-_j, S^z_k$ and then do the computation more carefully. c) What is the eigenvalue of $S^z_i$ on $\vert \Omega\rangle$?

  1. You're missing some terms in the third equality: the sum disappeared and you've dropped the terms where you take the commutators with the second spin operator in each product.

  2. a) That's correct. b) The result is nonzero if $l+1=n$. Hint: first work out the commutators between $S^+_i, S^-_j, S^z_k$ and then do the computation more carefully. c) Hint: what is the eigenvalue of $S^z_i$ on $\vert \Omega\rangle$?

Source Link
Jules Lamers
Jules Lamers
  • 607
  • 5
  • 16

  1. You're missing some terms in the third equality: the sum disappeared and you've dropped the terms where you take the commutators with the second spin operator in each product.

  2. a) That's correct. b) The result is nonzero if $l+1=n$. Hint: first work out the commutators between $S^+_i, S^-_j, S^z_k$ and then do the computation more carefully. c) What is the eigenvalue of $S^z_i$ on $\vert \Omega\rangle$?