# 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)

d

2

dt

2

⇀

r

r=

x+y

2

2

V(r)=-γexp(-r/a)

2

2

x

y

r=0

γ

a

x(t)

y(t)

x(0)

x'(0)

y(0)

y'(0)

x(t)

y(t)