1. A particle of mass m is in the environment of a force field with components: Fz=-Kz, Fy=Fx=0 for some constant K. Write down the Hamiltonian of the particle in Cartesian coordinates .What are the constant of motion? 2. H=kinetic energy +potential energy 3. Is the Hamiltonian H is just E= int(-K)dz = -Kz?? Also, I would like to ask what is the meaning of the constant of motion?? I really don't know where to start . That is the first time that I deal with the Hamiltonian Mechanics. I don't sure how to do the problem.