Title The Rough Molecule for IHS on Cone with Potential Type of Research Presentation Keywords Surface of Revolution, Rough Molecule, Hamiltonian systems, Potential eld. Abstract In this paper we extend the method of nding the rough molecules of the integrable hamiltonian system with two deegres of freedem on surface of revolution from compact case to non-compact case and we take cone as a surface of revoloution as an special example. Researchers Ghorbanali Haghighatdoost Bonab (First Researcher)، Jafar Ojbag (Second Researcher)