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In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown… (More)

A geometric approach to the method of Lagrange multipliers is presented using the framework of the tangent bundle geometry. The nonholonomic systems with constraint functions linear in the velocities… (More)

The virial theorem, introduced by Clausius in the field of statistical mechanics and later applied in both classical mechanics and quantum mechanics, is studied by making use of symplectic formalism… (More)

Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism.
Firstly, the case of canonoid… (More)

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 superposition rules, the… (More)

- Manuel F. Rañada
- 2014

The higher order superintegrability of the Tremblay–Turbiner–Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hyperbolic spaces, (κ > 0) and (κ… (More)

- Manuel F. Rañada
- 2012

The higher-order superintegrability of systems separable in polar coordinates is studied using an approch that was previously applied for the study of the superintegrability of a generalized… (More)

The existence of bi-Hamiltonian structures for the rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analysed by making use of the geometric theory… (More)

Abstract A nonlinear model of the quantum harmonic oscillator on two-dimensional space of constant curvature is exactly solved. This model depends on a parameter λ that is related with the curvature… (More)

A nonpolynomial one-dimensional quantum potential representing an oscillator, which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic… (More)