What is the simplest fermionic normalized quantum many-particle wavefunction, expressed in the first-quantized position representation, that you can think of? The normal single-particle examples don't seem to be that simple: Slater determinant of Gaussians times Hermite polynomials for harmonic oscillator, the free particle is not normalizable, and the infinite square well doesn't seem any better.
I understand simple in a fairly intuitive way: easy to manipulate, possible to differentiate and integrate, not too many symbols etc..
The best candidate I can think of (which is still not that good according to my example criteria above) is a single full Laundau level for a charged particle in a magnetic field, expressed as
in terms of complex coordinates $z=x+iy$ and with physical constants set to 1 (normalization from Wikipedia).
Do you know a simpler one?
I'm asking because I would like a simple one to test out concepts and understanding.