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A quantum carpet

This is the space-time diagram of a particle in a box in one dimension. Horizontal axis is the space coordinate, vertical axis is the time. The box consists of two inpenetrable walls to the left and to the right of the image. The initial wave function (the line at the bottom of the image) is the function which is constant inside the box. The motion of the wave function is periodic with period T=4/Pi. The time on the top of the image is 1/8 T (the period of the particle's state).

Here you can find a movie of this process.

General information about quantum carpets can be found in the article

Berry, M V, Marzoli, I and Schleich, W, 2001 ‘Quantum carpets, carpets of light’ Physics World (June), 39-44. (pdf).

More on the theory of the particle in a box can be found in the following article:

Berry, M V, J.Phys.A 29 6617-6629, ‘Quantum fractals in boxes’. (pdf)