assignment6

assignment6 - Problem Set 06 Note: This problem set is due...

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Problem Set 06 Note: This problem set is due Oct 18 before midnight. Please leave it in my mailbox located at the Frst ±oor of Rutherford building. 1. In the class we discussed the representation of the angular momentum generators 1 J x , J y and J z in terms of spin 1 2 and spin 1 states in Fnite dimensional Hilbert spaces. Determine the matrix representations of these generators in terms of spin 3 2 states. 2. In a n -dimensional Hilbert space I give you a Hermitian operator A whose eigenvalues are λ i with i = 1 , ..., n such that λ 1 λ 2 λ 3 .... λ n . (1) Show that in this space a generic vector | ψ i with the normalisability condition h ψ | ψ i = 1 always satisFes the following relation: λ 1 ≤ h ψ | A | ψ i ≤ λ n . (2) 3. One usefulness of writing the angular momentum operators in terms of spin 1 2 repre- sentations is that any traceless representation of an operator A can be written as a linear combinations of J i in the following way: A = α 1
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assignment6 - Problem Set 06 Note: This problem set is due...

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