arXiv subjects

Marco A. Reyes

Publications and source records attributed to Marco A. Reyes.

7 recordsLinked to original sources

arXiv2018

On the analytical solutions of the quasi-exactly solvable Razavy type potential V(x) = Vo (sinh4(x)-k sinh2(x) )

In order to show how stringent the restrictions posed on analytical solutions of quasi-exactly solvable potentials are, we construct analytical solutions for the Razavy type potential V(x) = Vo (sinh**4(x)-k sinh**2(x) ) based on the polynomial solutions of the related Confluent Heun Equation, where the free parameter k allows to tune energy eigenvalues, a desirable feature in different theories. However, we show that with the described method, the energy eigenvalues found diverge when k (goes to) -1, a feature caused solely by the procedure.

hep-th↗

arXiv2015

Supersymmetric features of the Error and Dawson's functions

Following a letter by Bassett, we show first that it is possible to find an analytical approximation to the error function in terms of a finite series of hyperbolic tangents from the supersymmetric (SUSY) solution of the Poschl-Teller eigenvalue problem in quantum mechanics (QM). Afterwards, we show that the second order differential equation for the derivatives of Dawson's function can be found in another SUSY related eigenvalue problem, where the factorization of the simple harmonic oscillator Hamiltonian renders the wrong-sign Hermite differential equation, and that Dawson's second order differential equation possess a singular SUSY type relation to this equation.

math-ph↗

arXiv2014

Fixed target experiments at the Fermilab Tevatron

This paper presents a review of the study of Exclusive Central Production at a Center of Mass energy of $\sqrt{s}=40$ GeV at the Fermilab Fixed Target program. In all reactions reviewed in this paper, protons with an energy of 800 GeV were extracted from the Tevatron accelerator at Fermilab and directed to a Liquid Hydrogen target. The states reviewed include $π^+π^-$, $K^0_s K^0_s$, $ K^0_sK^\pmπ^\mp$, $ϕϕ$ and $D^{*\pm}$. Partial Wave Analysis results will be presented on the light states but only the cross section will be reviewed in the diffractive production of $D^{*\pm}$

hep-ex↗

arXiv2010

Factorization procedure and new generalized Hermite functions

We propose an alternative factorization for the simple harmonic oscillator hamiltonian which includes Mielnik's isospectral factorization as a particular case. This factorization is realized in two non-mutually adjoint operators whose inverse product, in the simplest case, lead to a new Sturm-Liouville eigenvalue equation which includes Schrodinger's equation for the oscillator and Hermite's equation as particular cases for limiting values of the factorization's parameter, and whose eigenfunctions allow us to define new generalized Hermite functions.

math-ph↗

arXiv2008

On exact solutions to the scalar field equations in standard cosmology

A simple algebraic method to obtain exact solutions to the scalar field equations in spatially flat FRW cosmology is derived. The field potential fuction is reduced to two terms which can be used to determine some characteristic inflationary variables. To demonstrate the method, exact solutions resembling typical potentials of general interest are worked out. Finally, it is shown that this method of solution is also applicable to a perfect fluid in the same metric, for a curvature k>=0 and fixed gamma.

gr-qc↗

arXiv1997

Squeezed States and Helmholtz Spectra

The 'classical interpretation' of the wave function psi(x) reveals an interesting operational aspect of the Helmholtz spectra. It is shown that the traditional Sturm-Liouville problem contains the simplest key to predict the squeezing effect for charged particle states.

quant-ph↗

arXiv1995

The Classical Schrodinger's Equation

A non perturbative numerical method for determining the discrete spectra is deduced from the classical analogue of the Schrodinger's equation. The energy eigenvalues coincide with the bifurcation parameters for the classical orbits.