Hamiltonian function

From Vectorcalcumb

The total energy function. (pg. 65-66)

In a closed physical system the energy of the system is constant as the system moves through time.

Example: Ball being thrown into air: Total energy = p^2/2m +mgr (kinetic + potential)

We call the total energy function the Hamiltonian Function, and denote it H.

For a particle of mass m moving on a line. Kinetic = p^2/2m. If the particle is moving under the influence of a conservative force, like gravity, then there is a potential energy, U, which is a function of position.

H:=p^2/2m+U(r)