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Quick question about Kronecker delta function

  1. Jun 1, 2013 #1
    So in the infinite square well, the eigenfunctions are ## \psi_n (x) = \sqrt{\dfrac{2}{a}} \sin \left( \dfrac{n \pi}{a} x \right) ##

    Each state is orthogonal to each other, and so ## \displaystyle \int \psi_m (x) ^* \psi_n (x) dx = \delta_{mn} ##

    Does this also hold if they were cosines?
     
  2. jcsd
  3. Jun 1, 2013 #2
    Yes, the cosines are also orthonormal.
     
  4. Jun 1, 2013 #3

    Bill_K

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    Science Advisor

    You should be able to easily prove this yourself. Just use the trig identity for cos A cos B, and do the integral.
     
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