Question

what is a wave function?

Answer 1

f(x)=sin(x)
or something like that.

Answer 2

a function that describes a wave, like what zhang wrote there can be more pieces to it though, like x = A sin(wt + theta)

Answer 3

A wave function is not the same thing as a periodical function, like sine or cosine. A wave function is the solution to the Schroedinger's wave equation, which represents a probability amplitude for finding a particle somewhere in space.