CoulombF
CoulombF[l,η,r]
gives the regular Coulomb wavefunction .
Details
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- 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 (3)
Solve the Coulomb wave equation:
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:
Properties & Relations (2)
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