Ok, so I am trying understand how to derive the following version of the Schrodinger Equation for QHO:
\frac{d^2u}{dz^2} + (2\epsilon-z^2)u=0
where
\ 1. z=(\frac{m\omega}{hbar})^{1/2}x and
\ 2. \epsilon= \frac{E}{hbar\omega}
I've started with the TISE, used a potential of...