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

A discussion on the properties of Gamow states

Producción CientíficaGamow states are vector states for the pure decaying part of a quantum resonance. We review and analyze the properties of Gamow vectors in different representations. In particular, we discuss the controversial problem of assigning a mean value of the energy for a Gamow state from several points of view. The question on whether a Gamow state is a pure state or not is also analyzed here, as has relevance on the assignation of a non-zero value for the entropy for a Gamow state.Física Teórica, Atómica y Óptic

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

Gamow states as solutions of a modified Lippmann-Schwinger equation

Física Teórica, Atómica y Óptic

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 variational modification of the Harmonic Balance method to obtain approximate Floquet exponents

Producción CientíficaWe propose a modification of a method based on Fourier analysis to obtainthe Floquet characteristic exponents for periodic homogeneous linear systems,which shows a high precision. This modification uses a variational principle tofind the correct Floquet exponents among the solutions of an algebraic equation.Once we have these Floquet exponents, we determine explicit approximatedsolutions. We test our results on systems for which exact solutions are knownto verify the accuracy of our method including one-dimensional periodicpotentials of interest in quantum physics. Using the equivalent linear system,we also study approximate solutions for homogeneous linear equations withperiodic coefficients.Ministerio de Ciencia e Innovación (proyect PID2020-113406GB-I0), with funding from the European Union NextGenerationEU and Consejería de Educación through QCAYLE (PRTRC17.I1)National University of Rosario (Argentina) grant ING19/i40