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.
Examples
open allclose allBasic Examples (4)
Scope (19)
Numerical Evaluation (4)
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.
CMS
Wolfram Language. 2021. "CoulombF." Wolfram Language & System Documentation Center. Wolfram Research. 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