Main Question or Discussion Point
My own question, carried to a new thread as not to derail another:
This brings another question to mind, regarding whether that information (time) is already implicitly present [in the time-independent Schroedinger equation]. In modern physics is it as easy to integrate time into an equation as it is with classical physics?
My line of thought being that if you have the Hamiltonian, you have momentum, which contains velocity, which can be separated and integrated as dx/dt to introduce a time-dependence.
I've seen the formula for the time-dependent equation, but I haven't followed the mathematical development of it. I've only really worked with the one-dimensional, time-independent schrodinger equation... and the math is still shaky for me.