A particle wavefunction is like a really confusing to-do list. It's a wave that's also a particle, but not really. It's like, uh, never mind, just look at this diagram:
Anyway, here's a list of particle wavefunctions that will probably make your head hurt:
And, just for kicks, here's a random particle wavefunction:
The wavefunction of a single electron in a one-dimensional box is:
ψ(x) = Ae^(-2a^2)
Where A is some constant that's not really important right now, and a is a dimensionless constant that's definitely not important either.
But don't worry, it's all just math, and math is just a series of confusing symbols that will never make sense to anyone, including you.