We can take the Klein-Gordon equation describing the evolution of a complex scalar field. Taking the non-relativistic limit yields a classical wave equation that is identical in form to the Schrodinger equation.
We can also quantise the Klein-Gordon equation into a quantum field, and then, in the non-relativistic single particle special case, we end up with the actual free particle non-relativistic Schrodinger equation, complete with a probabilistic interpretation
What's the big picture? Why does doing either of these things produce equations of the same structure? And specifically what about the second approach results in a probabilistic interpretation?
