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Homework Help: Orthogonality question

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data

    If you want to show two wavefunctions are orthogonal, do you have to normalize the wavefunctions first then take the integral of the product and see if they're equal to 0?

    2. Relevant equations
    n/a


    3. The attempt at a solution
    not really applicable. I just want a explanation.
     
  2. jcsd
  3. Jan 25, 2010 #2
    Nope. Orthogonality just requires the inner product to be zero.

    A good visualization (though not in Hilbert space): In Euclidean 3-space (where inner product is the dot product) orthogonal vectors are perpendicular. Normalization scales vectors to the unit length. Heres the point: two vectors are perpendicular (orthogonal) regardless of their magnitude.

    Normalized, orthogonal vectors have a name too: orthonormal.
     
  4. Jan 25, 2010 #3
    okay thank you for the help!
     
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