New superintegrable models with positiondependent mass from Bertrand's Theorem on curved spaces
Abstract
A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship between such Bertrand Hamiltonians and positiondependent mass systems is explicitly established. These results are illustrated through the example of a superintegrable (nonlinear) oscillator on a BertrandDarboux space, whose quantization and physical features are also briefly addressed.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 March 2011
 DOI:
 10.1088/17426596/284/1/012011
 arXiv:
 arXiv:1011.0708
 Bibcode:
 2011JPhCS.284a2011B
 Keywords:

 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 13 pages