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WOLFRAM|DEMONSTRATIONS PROJECT

Classical Motion and Phase Space for a Morse Oscillator

​
initial conditions
x
0
0.7
p
0
-0.5
time
0.001
This Demonstration illustrates the classical anharmonic motion of a particle governed by the Hamiltonian
H=
2
p
2m
+
2
D
e
(1-
-αx
e
)
, where
D
e
and
α
are the well depth (dissociation energy) and width, respectively. Here
x
(t)
and
p
(t)
are obtained by solving Hamilton's equations of motion, subject to the initial conditions
x
0
=
x
(0)
and
p
0
=
p
(0)
. The three panels animate synchronously: (1) the motion of the particle in the potential; (2) the phase space trajectory; and (3) the time series of
x
(t)
and
p
(t)
. In the upper two panels, the points with minimum (turning points) and maximum momentum are labeled with blue and green
x
's, respectively.
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