Quantum Scattering in Two Dimensions

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Run
Speed:
Brightness:
Packet energy = 0.050
Reset
Barrier type:
Strength = 0.100
Size = 40
Softness = 0
Steps per second = 0

This program simulates scattering of a quantum particle from a stationary barrier in two dimensions. The particle’s initial state is a Gaussian wavepacket, whose average energy you can adjust. You can choose from seven different barrier shapes, and adjust their properties. Try a variety of settings to explore reflection, transmission, tunneling, and interference.

The brightness of the wavefunction image indicates the wavefunction’s magnitude, while the color hue indicates the phase, going from red (pure real and positive) to light green (pure imaginary and positive) to cyan (pure real and negative) to purple (pure imaginary and negative) and finally back to red. Use the slider to adjust the overall brightness.

The simulation uses natural units in which the particle’s mass, Planck’s constant ℏ, and the (nominal) screen pixel width are all equal to 1. It works by integrating a discretized version of the time-dependent Schrödinger equation, with a grid spacing of one unit and a grid size of 400 × 400. The wavefunction is always zero along all edges of the square grid, so the particle is effectively trapped inside a 400 × 400 box.

This simulation is computationally intensive. Although you can run it on a mobile device, I recommend using a personal computer.

This is free, open-source software. Use your browser to view the source code and license.

Daniel V. Schroeder, Physics Dept., Weber State University

See also this simulation of barrier scattering in one dimension, and this simulation of two colliding particles.

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