Time-dependant Schrödinger Equation Help.

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SUMMARY

The discussion centers on implementing a computer program to analyze wave packet behavior in quantum mechanics, specifically focusing on reflection and tunneling through a barrier using the Time-Dependent Schrödinger Equation. The user recalls prior exposure to the Time-Independent Schrödinger Equation but seeks clarity on the Time-Dependent variant. The recommended numerical method for this project is the "split-operator FFT," which is effective for simulating quantum systems.

PREREQUISITES
  • Understanding of the Time-Dependent Schrödinger Equation
  • Familiarity with wave packet dynamics in quantum mechanics
  • Knowledge of numerical methods, specifically "split-operator FFT"
  • Basic programming skills for implementing simulations
NEXT STEPS
  • Research the implementation of the Time-Dependent Schrödinger Equation in computational physics
  • Learn about wave packet propagation and its implications in quantum mechanics
  • Study the "split-operator FFT" method in detail for numerical simulations
  • Explore programming languages and libraries suitable for quantum simulations, such as Python with NumPy
USEFUL FOR

Students and researchers in quantum mechanics, computational physicists, and programmers interested in simulating quantum phenomena will benefit from this discussion.

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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