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