Time-dependant Schrödinger Equation Help.

[castusalbuscor]

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?

 

[f95toli]

Look up "split-operator FFT", it is a numerical method which should work well for this problem.

 

[denian]

First of all, I would recommend reviewing the Time-Independent Schrödinger equation and its concepts before delving into the Time-Dependent Schrödinger equation. It is important to have a solid understanding of the basics before moving on to more complex equations.

For your project, you will need to write a computer program to simulate the behavior of a wave packet reflecting off a barrier. This will involve using the Time-Dependent Schrödinger equation, which describes the evolution of a quantum system over time.

To start, you will need to define the initial conditions of your wave packet, such as its position, momentum, and energy. Then, using the Time-Dependent Schrödinger equation, you can calculate how the wave packet will evolve over time.

As for the equations that would be useful for your project, you will need to use the Time-Dependent Schrödinger equation, as well as other equations from Quantum Mechanics such as the wave function, Hamiltonian operator, and probability density function. It would also be helpful to review concepts such as wave-particle duality, superposition, and tunneling.

To actually start on the project, I would suggest breaking it down into smaller tasks and setting a timeline for each task. This could include researching and understanding the necessary equations, designing and writing the computer program, and analyzing and interpreting the results.

Additionally, it may be helpful to consult with your professor or other experts in the field for guidance and clarification on any confusing concepts. Good luck with your project!