1274 E Classical Mechanics
The classical Hamiltonian is expressed in coordinates and momentum components. If
the potential energy depends only on the relative coordinates,H
1
2 M
(p^2 cx+p^2 cy+p^2 cz)+1
2 μ(p^2 x+p^2 y+p^2 z)+V(x,y,z) (E-37)wherepcxis the momentum component that is conjugate toxc,pxis the momentum
component that is conjugate tox, and so on. The Hamiltonian equations of motion are
separated so that the center-of-mass motion and the relative motion are separated.