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Journal Articles

Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions

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A. D. Alhaidari
Journal: Journal of Mathematical Physics
J. Math. Phys. 64, 033506 (2023)
https://doi.org/10.1063/5.0082567
Published: March 2023
View articletitled, Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions
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Journal Articles

A generating integral for the matrix elements of the Coulomb Green’s function with the Coulomb wave functions

Open Access
K. Dzikowski, O. D. Skoromnik
Journal: Journal of Mathematical Physics
J. Math. Phys. 61, 032103 (2020)
https://doi.org/10.1063/1.5119349
Published: March 2020
View articletitled, A generating integral for the matrix elements of the Coulomb Green’s function with the Coulomb wave functions
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Includes: Supplementary data
Journal Articles

Connection formulas between Coulomb wave functions

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David Gaspard
Journal: Journal of Mathematical Physics
J. Math. Phys. 59, 112104 (2018)
https://doi.org/10.1063/1.5054368
Published: November 2018
View articletitled, Connection formulas between Coulomb wave functions
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Journal Articles

New approach to folding with the Coulomb wave function

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L. D. Blokhintsev, A. S. Kadyrov, A. M. Mukhamedzhanov, D. A. Savin
Journal: Journal of Mathematical Physics
J. Math. Phys. 56, 052102 (2015)
https://doi.org/10.1063/1.4919674
Published: May 2015
View articletitled, New approach to folding with the Coulomb wave function
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Journal Articles

Non-homogeneous solutions of a Coulomb Schrödinger equation as basis set for scattering problems

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J. A. Del Punta, M. J. Ambrosio, G. Gasaneo, S. A. Zaytsev, L. U. Ancarani
Journal: Journal of Mathematical Physics
J. Math. Phys. 55, 052101 (2014)
https://doi.org/10.1063/1.4874115
Published: May 2014
View articletitled, Non-homogeneous solutions of a Coulomb Schrödinger equation as basis set for scattering problems
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Journal Articles

A special asymptotic limit of a Kampé de Fériet hypergeometric function appearing in nonhomogeneous Coulomb problems

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L. U. Ancarani, G. Gasaneo
Journal: Journal of Mathematical Physics
J. Math. Phys. 52, 022108 (2011)
https://doi.org/10.1063/1.3554698
Published: February 2011
View articletitled, A special asymptotic limit of a Kampé de Fériet hypergeometric function appearing in nonhomogeneous Coulomb problems
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Journal Articles

Solutions for confluent and double-confluent Heun equations

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Léa Jaccoud El-Jaick, Bartolomeu D. B. Figueiredo
Journal: Journal of Mathematical Physics
J. Math. Phys. 49, 083508 (2008)
https://doi.org/10.1063/1.2970150
Published: August 2008
View articletitled, Solutions for confluent and double-confluent Heun equations
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Journal Articles

Derivatives of any order of the confluent hypergeometric function F 1 1 ( a , b , z ) with respect to the parameter a or b

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L. U. Ancarani, G. Gasaneo
Journal: Journal of Mathematical Physics
J. Math. Phys. 49, 063508 (2008)
https://doi.org/10.1063/1.2939395
Published: June 2008
View articletitled, Derivatives of any order of the confluent hypergeometric function F 1 1 ( a , b , z ) with respect to the parameter a or b
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Journal Articles

Direct demonstration of the completeness of the eigenstates of the Schrödinger equation with local and nonlocal potentials bearing a Coulomb tail

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N. Michel
Journal: Journal of Mathematical Physics
J. Math. Phys. 49, 022109 (2008)
https://doi.org/10.1063/1.2830976
Published: February 2008
View articletitled, Direct demonstration of the completeness of the eigenstates of the Schrödinger equation with local and nonlocal potentials bearing a Coulomb tail
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Journal Articles

Phase-integral calculation of the phase of the regular Coulomb wave function F L ( η , ρ )

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Staffan Yngve
Journal: Journal of Mathematical Physics
J. Math. Phys. 47, 042104 (2006)
https://doi.org/10.1063/1.2189196
Published: April 2006
View articletitled, Phase-integral calculation of the phase of the regular Coulomb wave function F L ( η , ρ )
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Journal Articles

Coulomb wave functions with complex values of the variable and the parameters

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Aleksander Dzieciol, Staffan Yngve, Per Olof Fröman
Journal: Journal of Mathematical Physics
J. Math. Phys. 40, 6145–6166 (1999)
https://doi.org/10.1063/1.533083
Published: December 1999
View articletitled, Coulomb wave functions with complex values of the variable and the parameters
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Journal Articles

Phase-integral formulas for Coulomb wave functions with complex values of the variable and the parameters

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Aleksander Dzieciol, Staffan Yngve, Per Olof Fröman
Journal: Journal of Mathematical Physics
J. Math. Phys. 40, 6167–6177 (1999)
https://doi.org/10.1063/1.533084
Published: December 1999
View articletitled, Phase-integral formulas for Coulomb wave functions with complex values of the variable and the parameters
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Journal Articles

Solutions to a spheroidal wave equation

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B. D. B. Figueiredo, M. Novello
Journal: Journal of Mathematical Physics
J. Math. Phys. 34, 3121–3132 (1993)
https://doi.org/10.1063/1.530066
Published: July 1993
View articletitled, Solutions to a spheroidal wave equation
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Journal Articles

Analytical solutions to the generalized spheroidal wave equation and the Green’s function of one‐electron diatomic molecules

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J. W. Liu
Journal: Journal of Mathematical Physics
J. Math. Phys. 33, 4026–4036 (1992)
https://doi.org/10.1063/1.529853
Published: December 1992
View articletitled, Analytical solutions to the generalized spheroidal wave equation and the Green’s function of one‐electron diatomic molecules
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Journal Articles

Analytical evaluation of elastic Coulomb integrals

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Henk F. Arnoldus, Thomas F. George
Journal: Journal of Mathematical Physics
J. Math. Phys. 33, 578–583 (1992)
https://doi.org/10.1063/1.529792
Published: February 1992
View articletitled, Analytical evaluation of elastic Coulomb integrals
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Journal Articles

Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two‐center problem in molecular quantum mechanics

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E. W. Leaver
Journal: Journal of Mathematical Physics
J. Math. Phys. 27, 1238–1265 (1986)
https://doi.org/10.1063/1.527130
Published: May 1986
View articletitled, Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two‐center problem in molecular quantum mechanics
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Journal Articles

Bessel function expansions of Coulomb wave functions

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J. Humblet
Journal: Journal of Mathematical Physics
J. Math. Phys. 26, 656–659 (1985)
https://doi.org/10.1063/1.526602
Published: April 1985
View articletitled, Bessel function expansions of Coulomb wave functions
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Journal Articles

Coulomb‐modified scattering parameters for Coulomb‐plus‐separable potentials for all l

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J. W. de Maag, L. P. Kok, H. van Haeringen
Journal: Journal of Mathematical Physics
J. Math. Phys. 25, 684–692 (1984)
https://doi.org/10.1063/1.526176
Published: March 1984
View articletitled, Coulomb‐modified scattering parameters for Coulomb‐plus‐separable potentials for all l
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Journal Articles

An SL(2,C)‐invariant representation of the Dirac equation. II. Coulomb Green’s function

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Levere C. Hostler
Journal: Journal of Mathematical Physics
J. Math. Phys. 24, 2366–2373 (1983)
https://doi.org/10.1063/1.525985
Published: September 1983
View articletitled, An SL(2,C)‐invariant representation of the Dirac equation. II. Coulomb Green’s function
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Journal Articles

A spectral representation for Coulomb wavefunctions

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J. Townsend, G. Feldman, T. Fulton
Journal: Journal of Mathematical Physics
J. Math. Phys. 13, 1865–1868 (1972)
https://doi.org/10.1063/1.1665922
Published: December 1972
View articletitled, A spectral representation for Coulomb wavefunctions
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