I want to look at the complex wave function $\psi$ in quantum mechanics.
If a complex number $a + bi$ is multiplied by $i$ it is rotated by 90 degree in the complex plane.
What does this mean for a complex scalar field, i.e. the wave function $\psi$?
I know, that $i\psi$ is as well a solution of the Schrödinger equation, because it is a linear differential equation.
My questions are:
- What are the physical consequences, if one multiplies the wave function by $i$?
- Are there any examples of actual experiments/phenomena, where something like that happens?
- How can I depict the multiplication of the wave function by $i$?