Born rule states that the probability density of the wave function is equal to the square of the function over the given interval. I thought, "Why squared?". I came up with this:
"We know that the wave function tells us about the distribution of where and when a particle might be. We then need a way to show the probability distribution mathematically. We know that the probability is proportional to $\Psi$, but $\Psi$ can be negative or even complex. The simplest way we can deal with this is by using $\Psi^2$ instead. Changing to $\Psi^2$ doesn't change how the distribution is, so is changing it to $\Psi^3$ or $|\Psi|$ or $2\Psi$, etc. If $\Psi$ were not possibly complex, using $|\Psi|$ would've been enough. But, $\Psi$ can be complex, so there's that."
I'd like a feedback on this. Am I thinking about this right? Or am I missing some things?
