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I Normalizing Constant 3D Infinite Well

  1. Feb 20, 2016 #1

    RaulTheUCSCSlug

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    For time independent Schrodinger's equation in 3-D

    Where Enx,ny,nz=(nx/Lx2+ny/Ly2+nz/Lz2)(π2ħ2/2m
    and Ψnx,ny,nz=Asin(nxπx/Lx)sin(nyπy/Ly)sin(nzπz/Lz)

    How do I normalize A to get (2/L)^3/2?

    I don't think I understand how to normalize constants.
     
  2. jcsd
  3. Feb 20, 2016 #2

    blue_leaf77

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    A normalized state ##\psi## means that the total probability described by this state, ##|\psi|^2##, is equal to unity.
     
  4. Feb 20, 2016 #3

    RaulTheUCSCSlug

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    So when A is (2/L)^3/2 then |\psi|^2 is equal to one since the probability density must go to one?

    So to solve for A one would just go through |\psi|^2 = 1 then solve for A?
     
  5. Feb 20, 2016 #4

    jtbell

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    The integral of ##|\psi^2|## over all space (or equivalently, over the entire volume of the well, since ##\psi## must be zero outside the well) must equal 1 in order for ##\psi## to be normalized.
     
  6. Feb 21, 2016 #5

    blue_leaf77

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    No, not that which must be equal to 1. Take a look at jtbell's comment above.
     
  7. Mar 13, 2016 #6

    RaulTheUCSCSlug

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    Right. So the purpose is to have the probability of the whole function sum up to 1. Okay. I went to office hours and got things clarified thank you!
     
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