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Axel Schulze-Halberg
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Journal Articles

Characterization of Darboux transformations for quantum systems with quadratically energy-dependent potentials

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 62, 083504 (2021)
https://doi.org/10.1063/5.0051739
Published: August 2021
View articletitled, Characterization of Darboux transformations for quantum systems with quadratically energy-dependent potentials
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Journal Articles

Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 61, 083502 (2020)
https://doi.org/10.1063/5.0013832
Published: August 2020
View articletitled, Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class
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Journal Articles

Higher-order Darboux transformations and Wronskian representations for Schrödinger equations with quadratically energy-dependent potentials

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 61, 023503 (2020)
https://doi.org/10.1063/1.5126431
Published: February 2020
View articletitled, Higher-order Darboux transformations and Wronskian representations for Schrödinger equations with quadratically energy-dependent potentials
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Journal Articles

Higher-order Darboux transformations for the massless Dirac equation at zero energy

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 60, 073505 (2019)
https://doi.org/10.1063/1.5095151
Published: July 2019
View articletitled, Higher-order Darboux transformations for the massless Dirac equation at zero energy
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Journal Articles

Generalized Schrödinger equations with energy-dependent potentials: Formalism and applications

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Axel Schulze-Halberg, Özlem Yeşiltaş
Journal: Journal of Mathematical Physics
J. Math. Phys. 59, 113503 (2018)
https://doi.org/10.1063/1.5058145
Published: November 2018
View articletitled, Generalized Schrödinger equations with energy-dependent potentials: Formalism and applications
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Journal Articles

The generalized confluent supersymmetry algorithm: Representations and integral formulas

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Axel Schulze-Halberg, Özlem Yeşİltaş
Journal: Journal of Mathematical Physics
J. Math. Phys. 59, 043508 (2018)
https://doi.org/10.1063/1.5023234
Published: April 2018
View articletitled, The generalized confluent supersymmetry algorithm: Representations and integral formulas
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Journal Articles

Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential

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Axel Schulze-Halberg, Pinaki Roy
Journal: Journal of Mathematical Physics
J. Math. Phys. 58, 113507 (2017)
https://doi.org/10.1063/1.5001797
Published: November 2017
View articletitled, Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
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Journal Articles

Generalized quantum nonlinear oscillators: Exact solutions and rational extensions

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Axel Schulze-Halberg, Barnana Roy
Journal: Journal of Mathematical Physics
J. Math. Phys. 57, 102103 (2016)
https://doi.org/10.1063/1.4965226
Published: October 2016
View articletitled, Generalized quantum nonlinear oscillators: Exact solutions and rational extensions
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Journal Articles

Arbitrary-order Jordan chains associated with quantum-mechanical Hamiltonians: Representations and integral formulas

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 57, 023521 (2016)
https://doi.org/10.1063/1.4942450
Published: February 2016
View articletitled, Arbitrary-order Jordan chains associated with quantum-mechanical Hamiltonians: Representations and integral formulas
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Journal Articles

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

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Axel Schulze-Halberg, Jie Wang
Journal: Journal of Mathematical Physics
J. Math. Phys. 56, 072106 (2015)
https://doi.org/10.1063/1.4927258
Published: July 2015
View articletitled, Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners
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Journal Articles

Time dependent potentials associated with exceptional orthogonal polynomials

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Axel Schulze-Halberg, Barnana Roy
Journal: Journal of Mathematical Physics
J. Math. Phys. 55, 123506 (2014)
https://doi.org/10.1063/1.4903257
Published: December 2014
View articletitled, Time dependent potentials associated with exceptional orthogonal polynomials
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Journal Articles

The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

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Alonso Contreras-Astorga, Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 55, 103506 (2014)
https://doi.org/10.1063/1.4898184
Published: October 2014
View articletitled, The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
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Journal Articles

Rational extension and Jacobi-type Xm solutions of a quantum nonlinear oscillator

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Axel Schulze-Halberg, Barnana Roy
Journal: Journal of Mathematical Physics
J. Math. Phys. 54, 122104 (2013)
https://doi.org/10.1063/1.4835575
Published: December 2013
View articletitled, Rational extension and Jacobi-type Xm solutions of a quantum nonlinear oscillator
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Journal Articles

Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions

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Axel Schulze-Halberg, Christopher R. Gordon
Journal: Journal of Mathematical Physics
J. Math. Phys. 54, 042108 (2013)
https://doi.org/10.1063/1.4801812
Published: April 2013
View articletitled, Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
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Journal Articles

Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 53, 103519 (2012)
https://doi.org/10.1063/1.4759118
Published: October 2012
View articletitled, Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix
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Journal Articles

Two-dimensional magnetic Schrödinger equations, Darboux transformations and solutions of associated auxiliary equations

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 53, 082108 (2012)
https://doi.org/10.1063/1.4746813
Published: August 2012
View articletitled, Two-dimensional magnetic Schrödinger equations, Darboux transformations and solutions of associated auxiliary equations
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Journal Articles

Higher order Darboux transformations in two dimensions, linearizable auxiliary equations, and invariant potentials

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 52, 083505 (2011)
https://doi.org/10.1063/1.3620515
Published: August 2011
View articletitled, Higher order Darboux transformations in two dimensions, linearizable auxiliary equations, and invariant potentials
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Journal Articles

Darboux transformations for a generalized Dirac equation in two dimensions

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Ekaterina Pozdeeva, Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 51, 113501 (2010)
https://doi.org/10.1063/1.3505127
Published: November 2010
View articletitled, Darboux transformations for a generalized Dirac equation in two dimensions
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Journal Articles

Green’s functions and trace formulas for generalized Sturm–Liouville problems related by Darboux transformations

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 51, 053501 (2010)
https://doi.org/10.1063/1.3407605
Published: May 2010
View articletitled, Green’s functions and trace formulas for generalized Sturm–Liouville problems related by Darboux transformations
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Journal Articles

Intertwining relations and Darboux transformations for Schrödinger equations in ( n + 1 ) dimensions

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Axel Schulze-Halberg
Journal: Journal of Mathematical Physics
J. Math. Phys. 51, 033521 (2010)
https://doi.org/10.1063/1.3355198
Published: March 2010
View articletitled, Intertwining relations and Darboux transformations for Schrödinger equations in ( n + 1 ) dimensions
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