CoulombF
CoulombF[l,η,r]
gives the regular Coulomb wavefunction .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- CoulombF[l,η,r] is a solution of the ordinary differential equation
.
- CoulombF[l,η,r] is proportional to
near
.
- CoulombF[l,η,r] tends to
for large
and some phase shift
.
- CoulombF has a branch cut discontinuity in the complex
plane running from
to
.
- For certain special arguments, CoulombF automatically evaluates to exact values.
- CoulombF can be evaluated to arbitrary numerical precision.
- CoulombF automatically threads over lists.
- CoulombF can be used with Interval and CenteredInterval objects. »
Examples
open allclose allBasic Examples (4)
Scope (20)
Numerical Evaluation (5)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
CoulombF can be used with Interval and CenteredInterval objects:
Specific Values (3)
Visualization (3)
Function Properties (7)
Series Expansions (1)
Applications (2)
Wavefunction for the radial Schrödinger equation with Coulomb potential between two point particles with charges and
separated by a distance
and energy of relative motion
:
Verify that the wavefunction satisfies the Schrödinger equation for specific values of the energy and separation:
Construct a WKB approximation of CoulombF:
Text
Wolfram Research (2021), CoulombF, Wolfram Language function, https://reference.wolfram.com/language/ref/CoulombF.html (updated 2023).
CMS
Wolfram Language. 2021. "CoulombF." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/CoulombF.html.
APA
Wolfram Language. (2021). CoulombF. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoulombF.html