#functional analysis

Friend of mine was like "the logarithmic potential well is so much cooler than the 1/r potential well that we have to live with" (if we lived in 2d we'd use a logarithmic potential well instead, this was basically just a lament about how our 3d world is boring in this one hyperniche way)

So i spent some time writing out the whole Schrodinger Equation for the 2d logarithmic well. I'm sure someone has already solved this (it's an extremely natural case to think about, it's not particularly unreasonable to expect someone to come across this on their own) but i miiight still take a crack at it later.