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Time Evolution of a Quantum Free Particle in 1D

​
wave number k
1
time
0
This Demonstration shows the time evolution and dispersion relation of a 1D quantum free particle represented by
ψ(x,t)=
ϕ
k
(x)
-
E
k
t/ℏ
e
, where
ϕ
k
(x)=
1
2π
kx
e
and
E
k
=
2
ℏ
2
k
2m
are the eigenfunctions and energy levels, respectively, for
-∞<k<∞
. The upper graphics show two different visualizations of the complex function
ψ(x,t)
. On the left, the shape is
|ψ(x,t)|
, and the coloring is according to the argument, with the range
0
to
2π
corresponding to colors from red to magenta. On the right, the real and imaginary parts are shown individually. The lower graphic shows the quadratic dispersion relation,
ω(k)=
E
k
/ℏ
.
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