Classical Barrier Crossing and Phase Space
Classical Barrier Crossing and Phase Space
This Demonstration illustrates the classical motion of a particle governed by the Hamiltonian . Here and are obtained by solving Hamilton's equations of motion, subject to the initial conditions =x(0) and =p(0). The three panels animate synchronously: (1) the motion of the particle as it approaches the potential, (2) the phase space trajectory, and (3) the time series of and . In the upper two panels, the points with minimum momentum (turning points) are labeled with blue 's.
H=+
2
p
2m
-α
2
x
e
x(t)
p(t)
x
0
p
0
x(t)
p(t)
x