arXiv subjects

Arturo Ramos

Publications and source records attributed to Arturo Ramos.

22 records · Page 2Linked to original sources

arXiv2001

A new geometric approach to Lie systems and physical applications

The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be related with equations on a Lie group and with some connections in fiber bundles. We develop two methods for dealing with such systems: the generalized Wei--Norman method and the reduction method, which is very useful when particular solutions of the original problem are known. The theory is illustrated with some applications in both classical and quantum mechanics.

math-ph↗

arXiv2000

The partnership of potentials in Quantum Mechanics and Shape Invariance

The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate new factorizations from old ones using invariance under parameter transformations. The theory is illustrated with some examples.

math-ph↗

arXiv2000

Shape Invariant potentials depending on n parameters transformed by translation

Shape Invariant potentials in the sense of [Gendenshte\"ın L.É., JETP Lett. 38, (1983) 356] which depend on more than two parameters are not know to date. In [Cooper F., Ginocchio J.N. and Khare A., Phys. Rev. {\bf 36 D}, (1987) 2458] was posed the problem of finding a class of Shape Invariant potentials which depend on n parameters transformed by translation, but it was not solved. We analyze the problem using some properties of the Riccati equation and we find the general solution.

hep-th↗

arXiv1998

Integrability of Riccati equation from a group theoretical viewpoint

In this paper we develop some group theoretical methods which are shown to be very useful for a better understanding of the properties of the Riccati equation and we discuss some of its integrability conditions from a group theoretical perspective. The nonlinear superposition principle also arises in a simple way.

math-ph↗