O M Friesch et al 2000 New J. Phys. 2 4 doi:10.1088/1367-2630/2/1/004
O M Friesch
, I Marzoli
and W P Schleich![]()
Video sequence 1
In this movie we present the time evolution of the probability
density
(x, t)|2 to find the
particle at time t at
position x in a box of width L. The initial wave function
is a Gaussian wave packet, centred around
= L /4,
having
width
= L /20 and an average momentum
= 15
/L. To
illustrate
the regularity in the wave packet
dynamics, we have placed two arrows, moving with constant velocity,
underneath the position axis. The left-hand arrow always points
to a minimum in the probability density (canal), while the
right-hand arrow is sometimes at a minimum and sometimes at a maximum
(chopped ridge). The rectangular bar on the left-hand side indicates
time. We have marked on it important fractions of the revival
time T, at which we can observe the fractional revivals of the
wave packet. Especially remarkable are the revivals occurring
at T /6 and T /4, characterized, respectively, by the
appearance of three and two replicas of the original wave packet.
Video sequence 2
The upper part of this animation shows the time evolution of
the Wigner function, and the lower one shows the resulting
probability distribution of finding the particle in the box. The
Wigner function is plotted in phase space, where the horizontal
axis corresponds to position and the vertical axis, on which we
have marked the zero, corresponds to momentum. Positive values are
displayed in orange, and negative ones are shown in blue. The movie
starts from the situation depicted in
figure 4 and
follows the dynamics up to t = T /2, when the wave packet
reshapes itself. Also, the time evolution of the Wigner function
is characterized by fractional revivals culminating in the full
revival at T /2.
Video sequence 3
We concentrate on the enlarged view of the central part of the
Wigner function, around momentum p = 0. This magnified
portion encompasses interference terms with momentum ranging
from -3p1 to 3p1. In the lower diagram,
we follow the
simultaneous weaving of the quantum carpet. To make clear the
correspondence between the interference terms of the Wigner
function and the world lines in the probability distribution, we
mark, with the same colour, the components of the Wigner
function with momenta ±p1 and the corresponding
structures
in the carpet.
Video sequence 4
We show the same sequence as in the previous animation, but this
time we highlight the terms in the Wigner function with momenta
±2 p1 and the corresponding zig-zag patterns in the
quantum carpet.
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