Quantum Wavepackets

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Plot: Real/imag  Density/phase         Grid

Click/tap to add a new wavepacket. Drag vertically to change its shape and horizontally to change its momentum. Or use the controls at right for more careful adjustments.

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This simulation shows the time evolution of a one-dimensional, nonrelativistic quantum wavefunction that is built out of Gaussian wavepackets. There are no forces acting on the particle within the region shown. However, the wavefunction is always zero at the edges of the region, so the particle is effectively trapped in an infinitely deep potential well. When a wavepacket hits an edge it will reflect.

You can plot either the real and imaginary parts of the wavefunction (shown in orange and blue, respectively), or the probability density and phase, with the phase represented by hues 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.

What to look for: Notice how a wavepacket moves in the direction of increasing phase, although the phase velocity (of the individual waves within a packet) differs from the group velocity (of the packet as a whole). Notice how packets of different widths spread out at different rates. Notice how after this spreading, the wavelength is no longer uniform within the packet. Notice the interference patterns produced when packets overlap or reflect off the edges.

The simulation works by solving a discretized version of the time-dependent Schrödinger equation, as you can see by looking at the source code.

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

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