New Hamiltonians with closed orbits

By considering energy-dependent coupling constants, we arrive at a class of 'pseudo-free Hamiltonians' of the form H=p(2)/2m(r), where the effective m ass depends on the radius r. We prove that these Hamiltonians can reproduce the E not equal 0 and L not equal 0 orbits r = r(phi) of standard Hamilton ians with central potentials. In particular, two cases yield closed ellipti cal orbits but violate Kepler's law of areas. Other peculiarities and gener alizations are discussed. (C) 2000 Published dy Elsevier Science B.V. All r ights reserved.