Why is psi^* psi dx a probability density - Griffiths

[kuahji]

Justification of ψ*ψdx as probability density of particle between x and x+dx using light's E-field and diffraction by slit.

This isn't a homework problem, rather it was on the list of things to know for the exam. They don't really go over it in Griffiths Quantum Mechanics books. So are any good resources out there on this topic?

 

[kuahji]

I'll put what I know down as well. I know that light doesn't work with Schrödinger's Equation, because it's massless. The probability that a particle is in (x, x+dx)=|ψ(x,t)|^2 dx (comes from probability at a point being zero).

energy is proportional to E^2, from the pon. vector we know ExB~EB~E^2 & we can reason intensity is proportional to E^2 and also to the # of photons.

Where I'm really stuck is how to relate E^2 to ψ^2.