# Normalization with Frobenius Method

1. Dec 13, 2013

### quarkgazer

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.