Time-Dependent Schrodinger Eq: Integrating Time?

[Pythagorean]

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 Schrödinger equation... and the math is still shaky for me.

 

[genneth]

Volumes have been written on this subject -- google for it, and focus on the papers from peer reviewed journals -- there's quite a bit of crack all over on this topic. You might want to learn classical mechanics a little further -- Goldstein, Classical Mechanics is the classic (no pun intended) reference. Understanding the role of time in classical mechanics is a prerequisite before you move on to the much trickier situation in QM. Suffice to say that momentum and velocity have almost exactly nothing to do with each other.