ListarDivisión de Nanociencias y Materiales por tema "Riccati equation"
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An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators
(2012)"We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators ... -
Factorization method for some inhomogeneous Lienard equations
(Sociedad Mexicana de Física, A. C., 2021)"The factorization of inhomogeneous Li\'enard equations is performed showing that through the factorization conditions involved in the method one can obtain forcing terms for which closed-form solutions exist. Because of ... -
Generalized Cornu-type spirals and their Darboux parametric deformations
(Elsevier, 2019)"We generalize the Fresnel integrals and introduce a class of spirals F-n, which contains the Cornu spiral as the case F-2. Their Darboux parametric deformations are also investigated. The F-3 spiral and some of its Darboux ... -
Multifractal analysis of the symmetry of a strictly isospectral energy landscape on a square lattice
(Elsevier, 2021)"We use the Höder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is two-dimensional and ... -
One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form
(2014)"In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F ◦ f)(x) = F(f(x)) and obtain a generalized Mielnik construction of one-parameter ... -
One-parameter isospectral special functions
(2003)"Using a combination of the ladder operators of Pina [1] and the Pammetric operators of Mielnik [2] we introduce second order linear differential equations whose eigenfunctions are isospectral to the special functions of ... -
Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients
(Elsevier, 2010)"We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically-coupled second-order differential equations. We solve ... -
Supersymmetry of FRW barotropic cosmologies
(2006)"Barotropic FRW cosmologies are presented from the standpoint of nonrelativis-tic supersymmetry. First, we reduce the barotropic FRW system of diferential equations to simple harmonic oscillator diferential equations. ...