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Integral of a Hermitian squared?

  1. Oct 31, 2012 #1
    1. The problem statement, all variables and given known data

    Compute: ∫x2(Hn(x))2e-x2dx

    The boundaries of the integral are -∞ to +∞

    2. Relevant equations

    By Rodrigues' formula:

    Hn(x) = (-1)nex2dn/dxn(e-x2)

    3. The attempt at a solution

    I proceed to plug in my expression for H into the integral, however, I'm insure as to what happens to the dependent derivative/integral when the derivative is squared. I believe the solution to this problem is straight "plug and chug." I got stuck pretty early and don't want to proceed until i know what to do with the derivative.

    Thanks in advance for your help!
     
  2. jcsd
  3. Nov 1, 2012 #2
    The Hermitian operator is supposed to be orthonormal. However, I am not familiar with it. Since you have the Hermitian squared, the integral should be 1
     
  4. Nov 1, 2012 #3

    Dick

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    Science Advisor
    Homework Helper

    The post is about Hermite polynomials, not Hermitian operators.
     
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