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Unformatted text preview: ’s in there, do one oF them as in (3.44) and now carry out the second ∂/∂x . This should give you a ˆ p 2 A . ²rom there, construct ∆ p = r a ˆ p 2 A − a ˆ p A 2 . 4. Extra credit: ∆ x ∆ k for a “hat” Let f ( x ) = a + x x ∈ [ − a, 0] a − x For x ∈ [0 , a ]  x  > a . Compute a x A , a x 2 A , and so, ∆ x, where a anything A ≡ i anything ·  f ( x )  2 dx i  f ( x )  2 dx . Find the Fourier transform ˜ f ( k ) ≡ I e − ikx f ( x ) dx. For this ˜ f , compute a k A , a k 2 A , and so, ∆ k. What is ∆ x ∆ k ? You should read: Libo±, Chapter 3. 2...
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 Spring '09
 Mucciolo
 Physics, mechanics, Uncertainty Principle, Englishlanguage films, Liboﬀ Problem

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