114 citations · 359 across the 14 of their papers we have counts for
14 papers
Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states
Alonso Contreras-Astorga, David J. Fernández C., César Muro-Cabral
In this work, we generate a family of quantum potentials that are non-rational extensions of the harmonic oscillator. Such a family can be obtained via two different but equivalent…
Solutions to the Painlevé V equation through supersymmetric quantum mechanics
David Bermudez, David J. Fernández C., Javier Negro
In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlevé V (PV) equation, a second-order non-linear o…
Complex oscillator and Painlevé IV equation
David J. Fernandez C, J. C. Gonzalez
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second- order supe…
Supersymmetric quantum mechanics and Painleve equations
David Bermudez, David J. Fernández C
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will defi…
Factorization method and new potentials from the inverted oscillator
David Bermudez, David J. Fernandez C
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator pot…
Harmonic Oscillator SUSY Partners and Evolution Loops
David J. Fernández C
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family o…
Solution hierarchies for the Painleve IV equation
David Bermudez, David J. Fernandez C
In this article we will obtain real and complex solutions to the Painleve IV equation through supersymmetric quantum mechanics. Then we will classify them into real solution hierar…
Complex solutions to Painleve IV equation through supersymmetric quantum mechanics
David Bermudez, David J. Fernandez C
In this work, supersymmetric quantum mechanics will be used to obtain complex solutions to Painleve IV equation with real parameters. We will also focus on the properties of the as…
Wronskian differential formula for confluent supersymmetric quantum mechanics
David Bermudez, David J. Fernandez C., Nicolas Fernandez-Garcia
A Wronskian differential formula, useful for applying the confluent second-order SUSY transformations to arbitrary potentials, will be obtained. This expression involves a parametr…
Hyperconfluent third-order supersymmetric quantum mechanics
David J Fernandez C, Encarnacion Salinas-Hernandez
The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potent…
Coherent states for quadratic Hamiltonians
Alonso Contreras-Astorga, David J Fernandez C, Mercedes Velazquez
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows to identify directly the creation and annihilation opera…
Supersymmetric partners of the trigonometric Poschl-Teller potentials
Alonso Contreras-Astorga, David J Fernandez C
The first and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Poschl-Teller potentials. The several…
Wronskian formula for confluent second-order supersymmetric quantum mechanics
David J. Fernandez C., Encarnacion Salinas-Hernandez
The confluent second-order supersymmetric quantum mechanics, for which the factorization energies tend to a single value, is studied. We show that the Wronskian formula remains val…
Higher-order supersymmetric quantum mechanics
David J Fernandez C, Nicolas Fernandez-Garcia
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order…