72 citations · 259 across the 11 of their papers we have counts for
7 papers · 1 filter
Nonlinear superpositions and Ermakov systems
José F. Cariñena, Javier de Lucas, Manuel F. Rañada
The theory of superposition rules for solutions of a Lie system of first-order differential equations is extended to deal with analogous systems of second-order and the theory is i…
Recent Applications of the Theory of Lie Systems in Ermakov Systems
José F. Cariñena, Javier De Lucas, Manuel F. Rañada
We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superp…
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
José F. Cariñena, Manuel F. Rañada, Mariano Santander
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are s…
Geometrization of Quantum Mechanics
J. F. Carinena, J. Clemente-Gallardo, G. Marmo
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum m…
Two important examples of nonlinear oscillators
José F. Cariñena, Manuel F. Rañada, Mariano Santander
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scatteri…
Group theoretical approach to the intertwined Hamiltonians
José F. Cariñena, David J. Fernández C., Arturo Ramos
We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered…