Coherent Gamow states for the hyperbolic Pöschl–Teller potential

Producción CientíficaWe have defined a pair of families of coherent states using creation and annihilation operators relating the Gamow states, vector states for non-relativistic quantum resonances. We have used an explicit one dimensional model, for which these operators may be explicitly written: the one dimensional P¨oschl-Teller Hamiltonian. We have shown that this model may serve as an example for the pseudo-boson formalism

Mathematical Foundations of Time Asymmetric Quantum Mechanics

Física Teórica. Atómica y Óptic

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

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A study of periodic potentials based on quadratic splines

Producción CientíficaIn this paper, we discuss a method based on a segmentary approximation of solutions of the Schrödinger equation by quadratic splines, for which the coefficients are determined by a variational method that does not require the resolution of complicated algebraic equations. The idea is the application of the method to one-dimensional periodic potentials. We include the determination of the eigenvalues up to a given level, and therefore an approximation to the lowest energy bands. We apply the method to concrete examples with interest in physics and discussed the numerical errors.2019-08-032019-08-03Ministerio de Economía, Industria y Competitividad (project MTM2014-57129)Junta de Castilla y León (programa de apoyo a proyectos de investigación - Ref. VA057U16

The definition of entropy for quantum unstable systems: a view-point based on the properties of Gamow states

Física Teórica. Atómica y Óptic

Evolution of quantum observables: from non-commutativity to commutativity

A fundamental aspect of the quantum-to-classical limit is the transition from a non- commutative algebra of observables to commutative one.However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infinite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.MINECO Grant MTM2014- 57129-C2-1-P. Junta de Castilla y Leon Grants BU229P18, VA137G18

Groups, Special Functions and Rigged Hilbert Spaces

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A modified Lyapunov method and its applications to ODE

Producción CientíficaHere, we propose a method to obtain local analytic approximate solutions of ordinary differential equations with variable coefficients, or even some nonlinear equations, inspired in the Lyapunov method, where instead of polynomial approximations, we use truncated Fourier series with variable coefficients as approximate solutions. In the case of equations admitting periodic solutions, an averaging over the coefficients gives global solutions. We show that, under some restrictive condition, the method is equivalent to the Picard-Lindelöf method. After some numerical experiments showing the efficiency of the method, we apply it to equations of interest in physics, in which we show that our method possesses an excellent precision even with low iterations.Ministerio de Ciencia e Innovación with funding from the European Union NextGenerationEU (PRTRC17.I1)Ministerio de Ciencia e Innovación project (PID2020-113406GB-I00