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WOLFRAM|DEMONSTRATIONS PROJECT

Motion in a Gaussian Potential

​
potential depth γ
37.2
gauss length a
3
mass m
1
x(0)
4
x'(0)
-1
y(0)
2
y'(0)
0
time
100
A mass
m
moves according to the nonrelativistic Newtonian motion equation
m
2
d
2
dt
r
=-gradV(r)
with
r=
2
x
+
2
y
in the central attractive Gaussian potential
V(r)=-γexp(-
2
r
2
a
)
. The angular momentum is time independent and the motion occurs in the
x
-
y
plane. The depth of the potential at
r=0
is
γ
(joule) and the spatial range
a
(meter). The Demonstration computes
x(t)
and
y(t)
. The four integration constants are
x(0)
,
x'(0)
,
y(0)
,
y'(0)
. The parametric plot of
x(t)
and
y(t)
depends on eight parameters.
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