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Unformatted text preview: and B are both Hermitian, then show that i( AB-BA ) is Hermitian as well. 5. (based on Chow 3.19) The Pauli spin matrices 1 := 0 1 1 0 , 2 := -i i and 3 := 1-1 play an important role in quantum mechanics. a. Show that each of these matrices is both Hermitian and unitary. Calculate the inverse of each. b. Show that the product of two Pauli matrices is i j = ij I + i X k ijk k , where ij and ijk are the Kronecker and Levi-Civita symbols, respectively. c. Calculate the commutator [ i , j ] of two Pauli matrices. 6. (Chow 3.21) Let A , B and C be square matrices of the same dimension. Show that tr AB = tr BA and tr ABC = tr BCA = tr CAB . Is tr ACB = tr ABC ?...
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This note was uploaded on 10/21/2011 for the course PHZ 3113 taught by Professor Staff during the Fall '10 term at FAU.
- Fall '10