Deriving hermite differential equation from schrødinger harm oscillator

[georg gill]

Homework Statement

I am trying to obtain the hermite polynomial from the schrødinger equation for a har monic oscillator. My attempt is shown below. Thank you! The derivation is based on this site:

http://www.physicspages.com/2011/02/08/harmonic-oscillator-series-solution/

The Attempt at a Solution

however the book says:

 

[blue_leaf77]

Seems like your mistake lies in your calculation of $\frac{\partial^2 \psi}{\partial y^2}$. I suggest that you check again on this point to see whether you had left out one term.

 

[georg gill]

thanks!