Wave Packets for Particle in a Box

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One of the simplest problems in quantum physics is that of a particle inside a one-dimensional box. This Demonstration shows the time evolution of a packet constructed as a superposition of the first standing waves. The coefficients are such that in the limit
the initial wave function would be a square pulse of half-width
located at
. With finite
these two parameters control the position and width of the initial wave packet. You can follow the time evolution of the real and imaginary parts of the wave function, the probability distribution function, and the real part of the
standing waves multiplied by their respective coefficients. The circles show the motion of the average position. Units:
, and the width of the box is 1.
Contributed by: Andrés Santos (December 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
In the chosen units, the standing wave functions are with
.
The (unnormalized) wave packet is , where
.
In the limit the initial wave packet
tends to a square pulse of half-width
located at
.
Permanent Citation