New Hamiltonians with closed orbits

Jamil Daboul, Mark Hickman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


By considering energy-dependent coupling constants, we arrive at a class of ‘pseudo-free Hamiltonians’ of the form H = p2/2m(r), where the effective mass depends on the radius r. We prove that these Hamiltonians can reproduce the E ≠ 0 and L ≠ 0 orbits r = r(φ) of standard Hamiltonians with central potentials. In particular, two cases yield closed elliptical orbits but violate Kepler’s law of areas. Other peculiarities and generalizations are discussed.

Original languageEnglish
Pages (from-to)232-239
Number of pages8
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number4
StatePublished - 20 Mar 2000


  • Boundary conditions
  • Closed orbits
  • Conservation laws
  • Energy-dependent potentials
  • Integrable models
  • Kepler law of areas
  • Runge-Lenz vector
  • Variable mass

ASJC Scopus subject areas

  • General Physics and Astronomy


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