That's why I utilised the Hertz vectors, this automatically sets the correct dependence the on ##\theta##. If we reconstruct the vector potential ##\mathbf{A}## we get
$$
\mathbf{A} = \nabla \times \boldsymbol{\Pi} = - \sin \theta \frac{\partial}{\partial r} \Pi_z(r,t) \hat{\boldsymbol{\phi}} =...
So I tried to solve this using the Hertz potentials. I choose the magnetic one since this one corresponds to the magnetisation.
Before I start let me note that I denote a unit vector with a hat, while ##{x,y,z}## are the Cartesian coordinates and ##{r,\theta,\phi}## are the spherical...
For clarity I finished the calculation using rules for Spin-Weighted Spherical harmonics and corrected a typo. I've modified the notebook and the pdf. But the problem of course remains.
Hello, the Homework Statement is quite long, since it includes a lot of equations so I will rather post the as images as to prevent mistypes.
We need to find the integral
where
with
$$
J_m =(\sqrt{2}(r−ia\cosθ))^{−1} i(r^2+a^2)\sin(θ)j,
$$
$$
J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...