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.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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