57 research outputs found
A System of n=3 Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion
The properties of a system of n = 3 coupled oscillators with linear terms in
the velocities (magnetic terms) depending in two parameters are studied. We
proved the existence of a bi-Hamiltonian structure arising from a
non-symplectic symmetry, as well the existence of master symmetries and
additional integrals of motion (weak superintegrability) for certain particular
values of the parameters.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach
The quantum free particle on the sphere () and on the
hyperbolic plane () is studied using a formalism that
considers the curvature \k as a parameter. The first part is mainly concerned
with the analysis of some geometric formalisms appropriate for the description
of the dynamics on the spaces (, \IR^2, ) and with
the the transition from the classical -dependent system to the quantum
one using the quantization of the Noether momenta. The Schr\"odinger
separability and the quantum superintegrability are also discussed. The second
part is devoted to the resolution of the -dependent Schr\"odinger
equation. First the characterization of the -dependent `curved' plane
waves is analyzed and then the specific properties of the spherical case are
studied with great detail. It is proved that if then a discrete
spectrum is obtained. The wavefunctions, that are related with a
-dependent family of orthogonal polynomials, are explicitly obtained
Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
The quantization of systems with a position dependent mass (PDM) is studied.
We present a method that starts with the study of the existence of Killing
vector fields for the PDM geodesic motion (Lagrangian with a PDM kinetic term
but without any potential) and the construction of the associated Noether
momenta. Then the method considers, as the appropriate Hilbert space, the space
of functions that are square integrable with respect to a measure related with
the PDM and, after that, it establishes the quantization, not of the canonical
momenta , but of the Noether momenta instead. The quantum Hamiltonian,
that depends on the Noether momenta, is obtained as an Hermitian operator
defined on the PDM Hilbert space. In the second part several systems with
position-dependent mass, most of them related with nonlinear oscillators, are
quantized by making use of the method proposed in the first part.Comment: 21 pages, to appear in J.Phys. A:Math. Theo
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