Wave functions are, of course, almost always complex-valued. In all of the examples that I have seen (infinite square well, etc.), the real part of the wave function and the imaginary part of the wave function are basically the same function (except for a phase difference and possibly a sign difference). Do you know of an example of a wave function, that is complex-valued, for which the real and imaginary parts are fundamentally different functions? (To be honest, I have not seen that many examples). Thanks in advance.