About a month ago, I discovered a previously unknown solution to the simplest Schrödinger equation for the hydrogen atom.
It turns out that this wavefunction:
where J₀ is the ordinary Bessel function J₀, solves this equation:
What I find more surprising about the result is that it solves one of the best known equations in mathematical physics, yet has apparently remained undiscovered for over a hundred years!
Here’s a preprint of a paper that I’m working on to explain the result: