4cos2x = 8sinxcosx
4cos2x - 8sinxcosx = 0
Now I am stuck. I don't know what identities to use. I can see it was set to 0 for a reason. But why?
I know the answer is
4 - 4tan2x = 0 but how?
Thanks.
That is exactly my point. Looking at the given equation and seeing that ##\frac {2E} {hw}## is negligible compared to ##y^2## you are supposed to guess the general solution... that ##\Psi(y)## will be as ##e^{\frac {-y^2} 2}##. Totally lost. Here is where I found this problem...
OK, so I get:
##\frac {d^2\Psi(y)} {dy^2} + (\frac {2E} {hw} - y^2)\Psi(y) = 0##
Then,
##\Psi(y) = u(y)e^{\frac {-y^2}{2}}## is the general solution.
Totally lost. Where did ##\frac{-y^2}2## come from?
Why do we have to replace ##\frac d {dx}## by ##\sqrt \frac {mw} h## ##\frac d {dy}## ? I can see we are changing from dx to dy because we are substituting in ##y\sqrt\frac h {mw}## for x? But where does ##\sqrt \frac {mw} h## come from? Is it the chain rule?