CoulombH2 [l,η,r]
gives the incoming irregular Coulomb wavefunction TemplateBox[{l, eta, r}, CoulombH2].
CoulombH2
CoulombH2 [l,η,r]
gives the incoming irregular Coulomb wavefunction TemplateBox[{l, eta, r}, CoulombH2].
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- CoulombH2 [l,η,r] is a solution of the ordinary differential equation .
- CoulombH2 [l,η,r] is proportional to for large .
- CoulombH2 [l,η,r] has a regular singularity at .
- CoulombH2 has a branch cut discontinuity in the complex plane running from to .
- For certain special arguments, CoulombH2 automatically evaluates to exact values.
- CoulombH2 can be evaluated to arbitrary numerical precision.
- CoulombH2 automatically threads over lists.
- CoulombH2 can be used with CenteredInterval objects. »
Examples
open all close allBasic Examples (5)
Scope (18)
Numerical Evaluation (5)
Evaluate numerically:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
CoulombH2 can be used with CenteredInterval objects:
Specific Values (3)
Visualization (2)
Plot the real and imaginary parts of CoulombH2 :
Plot the real part of TemplateBox[{2, 0, z}, CoulombH2]:
Plot the imaginary part of TemplateBox[{2, 0, z}, CoulombH2]:
Function Properties (6)
Series Expansions (1)
Function Representations (1)
Relations with other Coulomb functions:
Properties & Relations (1)
CoulombH2 is proportional to WhittakerW in some region of the complex plane:
However, the stated definition has a branch cut at , while the built-in CoulombH2 has a branch cut at :
Related Guides
Text
Wolfram Research (2021), CoulombH2, Wolfram Language function, https://reference.wolfram.com/language/ref/CoulombH2.html (updated 2023).
CMS
Wolfram Language. 2021. "CoulombH2." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/CoulombH2.html.
APA
Wolfram Language. (2021). CoulombH2. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoulombH2.html
BibTeX
@misc{reference.wolfram_2025_coulombh2, author="Wolfram Research", title="{CoulombH2}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/CoulombH2.html}", note=[Accessed: 03-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_coulombh2, organization={Wolfram Research}, title={CoulombH2}, year={2023}, url={https://reference.wolfram.com/language/ref/CoulombH2.html}, note=[Accessed: 03-January-2026]}