So I'm having problems with the double infinite potential well given by
I have to use the fact that the potential well is symmetric about $x=0$. I have solved the Schrödinger equation in all the regions and end up with
$$\psi1=A\sin(k_1x)+B\cos(k_1x)$$ $$\psi2=Ce^{k_2x}+De^{-k_2x}$$ $$\psi3=E\sin(k_1x)+F\cos(k_1x)$$
where $k_1=\sqrt{\frac{2mE}{\hbar^2}}$ and $k_2=\sqrt{\frac{2m(v_0-E)}{\hbar^2}}$. I Use the symmetry argument and get $C=D$ which means $cosh$ for even and $sinh$ for odd wave functions. I'm really struggling to normalise the piecewise wave functions... I know that I'm meant to get $A\sin(k_1(a+b-x))$ but I'm not sure how. So if I know how to do that it may help me normalise the wave function. Many thanks in advance!