I was recently introduced to wavefunctions in my freshman Modern Physics class. While discussing their properties, we often drew diagrams like this:
This was all fine until I was told that wavefunctions are complex functions. I take this to mean that the range is complex, but now this diagram makes little sense. How are complex numbers (with both a real and imaginary part) displayed on one axis (the vertical one in the diagram)? The problem gets worse since we then used such diagrams to look for discontinuities.
This is perhaps a silly question, but I can't find a way to make sense of this. Where am I going wrong?