I think I see where this is going now. Given that the final form of the expansion of ##(x-iy)^2## does not match the spherical harmonic (in terms of its Cartesian representation) of the wave function in question I would NOT expect to see ##Y_{2,-2}## in this particular wave function. So after...
See the picture below for details. I have included my solution thus far, but it doesn't feel right and I'm just wondering what I am missing. Any assistance would be greatly appreciated, cheers.
Science undergrad. majoring in physics. Recently changed to a combined BSc/BEng (aerospace engineering). Want to work for SpaceX or NASA some day, building rockets and spaceships with the end goal of getting into space myself. Boy is it hard work!