Problem%20Set%205%202008.1 - Problem Set 5 Due:00 pm 1...

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Problem Set # 5 Due. May 15 12:00 pm 1. Consider rotations about the x-axis: D(x; φ )=exp(-i φ /2)|x;+><x;+| + exp(i φ /2)|x; - ><x; - | (|x; ± > is the eigenstate of S x ) which performs rotations that you may have expected from purely geometric considerations. a) First consider rotations on an ordinary vector in three dimensions. Suppose that the vector is initially y v i ˆ = r and that this is rotated through an angle φ about the x-axis, resulting in a vector f v r . Determine an expression for f v r in terms of , and φ . x ˆ y ˆ b) Now consider operations on kets. Represent the rotation D(x; φ ) in the {|z;+> , |z;->}
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