Finding the magnetic field based on vector potential

1. Aug 15, 2011

jm16180339887

1. The problem statement, all variables and given/known data

If you have |$\psi$>=cos($\theta$/2)ei*l*$\varphi$/2+sin($\theta$/2)e-i*l*$\varphi$/2ei$\varphi$
and A=<$\psi$|$\partial$$\varphi$|$\psi$>$\hat{r}$
find B in polar coordinates
2. Relevant equations

B=$\nabla$xA

3. The attempt at a solution

So far I got B=$\frac{1}{r}$[-iei$\varphi$($\frac{l(l-1)}{4}$e(l-1)-$\frac{(1-l)(1-\frac{l}{2})}{2}$e(1-l))$\hat{\theta}$-($\frac{l}{2}$cos($\theta$/2)sin($\theta$/2)+$\frac{l}{4}$sin2($\theta$/2)ei$\varphi$(l-1)-$\frac{l}{4}$cos2($\theta$/2)ei$\varphi$(l-1)+($\frac{1}{2}$cos2($\theta$/2)-$\frac{1}{2}$sin2($\theta$/2)-$\frac{l}{4}$cos2($\theta$/2)+$\frac{l}{4}$sin2($\theta$/2)ei$\varphi$(1-l)-cos($\theta$/2)sin($\theta$/2)+$\frac{l}{2}$sin($\theta$/2)cos($\theta$/2))$\hat{\varphi}$]

but I was told that the answer is l+1. How do I simplify this equation?

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