Deformed algebras and effective Hamiltonians

ANGEL BALLESTEROS; ALFONSO BLASCO; OSVALDO CIVITARESE; FRANCISCO HERRANZ; MARTA REBOIRO

Salamanca

Congreso; Symmetries in Gravity and Field Theory; 2004

Universidad de Salamanca. España.

Deformed algebras are used to construct effective Hamiltonians for severalnonlinear quantum problems. In all the cases here presented, the deformationparameter can be fitted in such a way that the dynamical propertiesof the physical models are faithfully reproduced, despite the strong algebraicsolvability of the corresponding effective Hamiltonians. In particular,recent results concerning effective fermion-boson and boson-boson interactionHamiltonians defined through suq(2) and the Higgs algebra -respectively- arereviewed. A new correspondence between a q-oscillator and finite range potentialsis also described.