Time-dependant Schrödinger Equation Help.

castusalbuscor
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I have a project to work on that's due by mid March.

I would need to write a computer program, to show how a wave packet reflect off a barrier? How much of the wave reflects off a wall of finite height and thickness, and how much tunnels through?

I remember doing something similar in my first Quantum Mechanics class last term, but we only covered the Time-Independent Schrödinger equation, and I remember that the concepts got me slightly confused.

Unfortunately I do not own the Quantum Mechanics book, I borrowed one from one of the professors in the department.

What equations would be of great use to me? And how would I go about to actually start on the project?
 
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Look up "split-operator FFT", it is a numerical method which should work well for this problem.
 
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