On the Nonuniqueness of the Hamiltonian for Systems with One Degree of Freedom

Abstract

The alternative Hamiltonians for systems with one degree of freedom are solved directly from the Hamilton ’ s equations. These new Hamiltonians produce the same equation of motion with the standard one (called the Newtonian Hamiltonian). Furthermore, new Hamiltonians come with an extra-parameter, which can be used to recover the standard Hamiltonian.