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# HW3 - ’s in there do one oF them as in(3.44 and now carry...

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PHYSICS 4455 – QUANTUM MECHANICS Problem Set 3 – due 9/15/2005, in class. 1. Getting more familiar with δ functions. Liboff Problem 3.6 Remember to regard these equalities in the following sense. To show blah = BLAH , you need to demonstrate that integraldisplay blah · f ( y ) dy = integraldisplay BLAH · f ( y ) dy for any (infinitely differentiable) function f . 2. Gaussian wave packet. Liboff Problem 3.10. Ignore the “Argue... ” bit. (I have more or less shown you how to get this in class.) 3. More on the Gaussian packet. Liboff Problem 3.11 If you follow the rule of calculus verycarefully , you shouldn’t need the following Hints: Follow Liboff from line 1 in (3.44) to line 2, but write the latter in terms of x . Now, with two ∂/∂x ’s in there, do one of them as in

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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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