Trouble with normalizing a wave function

  • Thread starter marineric
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  • #1
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Homework Statement


A particle of mass m is in the state ψ(x,t) = Ae-a[mx2/h-bar)+it]

Find A

Homework Equations


I know that to normalize a wave function I should use ∫ψ2 = 1


The Attempt at a Solution


The book gives the solution as 1 = 2abs(A)2∫ e-2amx2/h-bar) dx

My question is where does the "2" factor in front of the A2 come from?
 

Answers and Replies

  • #2
954
117
Hmm...could you perhaps provide a little more information on
(i) the domain of the wavefunction
(ii) the bounds of that integral
 
  • #3
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i) the domain is for all x and t > 0?

ii) the bounds of the integral are from 0 to ∞
 
  • #4
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I think I got it. The solutions manual integrated from 0 to ∞, and multiplied by 2 because of symmetry (to get the -∞ to 0 part)
 
  • #5
954
117
I think I got it. The solutions manual integrated from 0 to ∞, and multiplied by 2 because of symmetry (to get the -∞ to 0 part)
Yup, seems like it. It is rather odd of them to do that though; usually we like -∞ to ∞ bounds because they allow us to use the Gaussian integration formula.
 

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