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

45[37.2,3,1,4,-1,2,0,

100]

A mass

m

moves according to the nonrelativistic Newtonian motion equation

m

d

2

dt

2

⇀

r

=-gradV(r)

with

r=

x

2

+y

2

in the central attractive Gaussian potential

V(r)=-γexp(-r

2

/a

2

)

. 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