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

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PHYSICS 4455 – QUANTUM MECHANICS Problem Set 3 – due 9/15/2005, in class. 1. Getting more familiar with δ functions. Libof Problem 3.6 Remember to regard these equalities in the Following sense. To show blah = BLAH , you need to demonstrate that i blah · f ( y ) dy = i BLAH · f ( y ) dy For any (in±nitely diferentiable) Function f . 2. Gaussian wave packet. Libof 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. Libof Problem 3.11 IF you Follow the rule oF calculus very carefully , you shouldn’t need the Following Hints: ²ollow Libof From line 1 in (3.44) to line 2, but write the latter in terms oF x . Now, with two ∂/∂x
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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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This note was uploaded on 11/09/2009 for the course PHY 4604 taught by Professor Mucciolo during the Spring '09 term at University of Central Florida.

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

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