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Classical Barrier Crossing and Phase Space

initial conditions

-2.5

0.5

time

0.001

This Demonstration illustrates the classical motion of a particle governed by the Hamiltonian

-α

. Here

x(t)

and

p(t)

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

x(t)

and

p(t)

. In the upper two panels, the points with minimum momentum (turning points) are labeled with blue

's.

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