30 citations · 224 across the 17 of their papers we have counts for
17 papers
Darboux transformations for Dunkl-Schroedinger equations with energy dependent potential and position dependent mass
Axel Schulze-Halberg, Pinaki Roy
We construct arbitrary-order Darboux transformations for Schroedinger equations with energy-dependent potential and position-dependent mass within the Dunkl formalism. Our construc…
Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators
Axel Schulze-Halberg, Pinaki Roy
We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and…
Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation
A. Schulze-Halberg, A. M. Ishkhanyan
We apply the Darboux transformation to construct new exactly-solvable cases of the two-dimensional massless Dirac equation for potential classes of Lambert-W and inverse exponentia…
Exactly-solvable quantum systems in terms of Lambert-W functions
A. Schulze-Halberg, A. M. Ishkhanyan
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schrödinger models wit…
Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
A. Schulze-Halberg, P. Roy
We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. After determining a modified ortho…
Construction of zero energy states in graphene through the supersymmetry formalism
Axel Schulze Halberg, Pinaki Roy
We devise a supersymmetry-based method for the construction of zero-energy states in graphene. Our method is applied to a two-dimensional massless Dirac equation with a hyperbolic…
Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
Axel Schulze-Halberg, Pinaki Roy
We introduce generalized versions of complex Scarf and Morse-type potentials that con- tain energy-dependent parameters. PT -symmetry and pseudo-hermiticity of the associated quant…
Recursive Representation of Wronskians in Confluent Supersymmetric Quantum Mechanics
Alonso Contreras-Astorga, Axel Schulze-Halberg
A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With th…
Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials
Axel Schulze-Halberg, Pinaki Roy
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based…
On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
Alonso Contreras-Astorga, Axel Schulze-Halberg
We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymme…
The generalized zero-mode supersymmetry scheme and the confluent algorithm
Alonso Contreras-Astorga, Axel Schulze-Halberg
We show the relationship between the mathematical framework used in recent papers by H.C. Rosu, S.C. Mancas and P. Chen (2014) and the second-order confluent supersymmetric quantum…
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
Alonso Contreras-Astorga, Axel Schulze-Halberg
We introduce the confluent version of the quantum-mechanical supersymmetry (SUSY) formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to sp…
DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
Axel Schulze-Halberg, Barnana Roy
We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Pr…
Rational extension and Jacobi-type {\boldmath{}} solutions of a quantum nonlinear oscillator
Axel Schulze-Halberg, Barnana Roy
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum a…
An exactly-solvable three-dimensional nonlinear quantum oscillator
Axel Schulze-Halberg, John R. Morris
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dep…
Propagators of Generalized Schrödinger Equations Related by Higher-Order Supersymmetry
Ekaterina Pozdeeva, Axel Schulze-Halberg
We construct explicit integral relations between propagators of generalized Schrödinger equations that are linked by higher-order supersymmetry. Our results complement and extend t…
Darboux transformation for a general Dirac equation in two dimensions
Ekaterina Pozdeeva, Axel Schulze-Halberg
We construct explicit Darboux transformations for a generalized, two-dimensional Dirac equation. Our results contain former findings for the one-dimensional, stationary Dirac equat…