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Normalization with Frobenius Method

  1. Dec 13, 2013 #1
    Hi, I have a ground state wavefunction, $$ \psi_0(\xi) = A_0\exp(-\frac{1}{2}\alpha\xi^2), $$ (##\alpha## is a constant) and I have used the method of Frobenius to find the successive solutions: $$ \psi_n(\xi) = \Gamma_n(\xi)\exp(-\frac{1}{2}\alpha\xi^2) $$ where ## \Gamma_n(\xi) = \sum\limits_{\nu=1}^{\infty} \beta_\nu \xi^\nu ##. I will not include the details at this point but I can define a recurrence relation for ## \Gamma_n(\xi) ## that reduces ## \Gamma_n(\xi) ## to a polynomial (for each ## n ##).

    How do I go about normalizing ##\psi_n(\xi)##?

    Thanks in advance for any help. It is much appreciated.

    PS: I have looked into Hermite polynomials for comparison but I am still unsure of the normalization.
     
  2. jcsd
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