PS7_key.pdf - Problem Set 7 1 1 ψ(k = ∞ 2π 1 = = ψ(x...

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Problem Set 7 1. ψ ( k ) = 1 2 π - ψ ( x ) e k x x = 1 2 π 2 a - a 2 a 2 cos π x a e - k x x = 1 2 π 2 a - a 2 a 2 e ⅈ π x / a + e - ⅈ π x / a 2 e - k x x = 1 2 a π - a 2 a 2 e ⅈ π x / a + e - ⅈ π x / a e - k x x = 1 2 ⅈ  π a - k a π e ⅈ  π a - k x - a 2 a 2 - 1 2 ⅈ  π a + k a π e - ⅈ  π a + k x - a 2 a 2 = 1 π a - k a π sin π a - k a 2 + 1 π a + k a π sin π a + k a 2 = 2 a π ( π 2 - a 2 k 2 ) cos a k 2
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In[18]:= ψ [ x _ , a _] : = Piecewise  2 a Cos π a x , x a 2 && x - a 2 , 0, x < - a 2 || x > a 2  ; 1 2 π - a 2 a 2 2 a Cos π a x E k x x (* Check that the ψ ( k ) we calculated above is correct. *) ψ [ k _] : = 2 a π Cos a k 2 (- a 2 k 2 + π 2 ) ; - Conjugate ψ [ k ]  ψ [ k ] k (* Check that ψ ( k ) is normalized ( for a > 0 ) . *) Plot Conjugate ψ [ k ]  ψ [ k ] / . a 100, { k, - 0.2, 0.2 } Out[19]= 2 π Cos a k 2 1 a (- a 2 k 2 + π 2 ) Out[21]= ConditionalExpression
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  • Fall '18
  • Pallavolo Modena, Heisenberg, Ψ, 50 k, 0.03, 2 - k

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