# hw4 - σ x to σ y and σ z Can you see a connection to a...

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Homework 4 PHZ 3113 Due Monday, February 8, 2010 Chapter 3 1. The Pauli matrices below are related to the spin of a spin 1 / 2 particle σ x = 0 1 1 0 σ y = 0 - i i 0 σ z = 1 0 0 - 1 a) Show that the Pauli matrices are unitary and Hermitian b) Find the eigenvectors and eigenvalues, and the unitary transformation matrix U and U for σ x and σ y . Note that σ z is already diagonal. c) Compute the commutators [ σ x , σ y ],[ σ y , σ z ], and [ σ z , σ x ] d) Use the eigenstates of σ x as a basis, and rewrite σ x , σ y , and σ z in this new basis. (Hint: Simply apply the similarity transformation generated by diagonalizing
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Unformatted text preview: σ x to σ y and σ z .) Can you see a connection to a rotation about the y-axis? 2. Boas, Chapter 3, Section 6, Prob. 20 3. Boas, Chapter 3, Section 7, Prob. 26 4. Boas, Chapter 3, Section 7, Prob. 27 5. Boas, Chapter 3, Section 8, Prob. 4 6. Boas, Chapter 3, Section 8, Prob. 25 7. Boas, Chapter 3, Section 11, Prob. 16 8. Boas, Chapter 3, Section 12, Prob. 16 1...
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