Computes the regular Coulomb wave function.

Namespace: Meta.Numerics.Functions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.1.0.0 (2.1.0.0)

Syntax

            
 C#  Visual Basic  Visual C++  F# 
public static double CoulombF(
	int L,
	double eta,
	double rho
)
Public Shared Function CoulombF ( _
	L As Integer, _
	eta As Double, _
	rho As Double _
) As Double
public:
static double CoulombF(
	int L, 
	double eta, 
	double rho
)
static member CoulombF : 
        L : int * 
        eta : float * 
        rho : float -> float 

Parameters

L
Int32
The angular momentum number, which must be non-negative.
eta
Double
The charge parameter, which can be postive or negative.
rho
Double
The radial distance parameter, which must be non-negative.

Return Value

The value of FL(η,ρ).

Remarks

The Coulomb wave functions are the radial wave functions of a non-relativistic particle in a Coulomb potential.

They satisfy the differential equation:

A repulsive potential is represented by η > 0, an attractive potential by η < 0.

F is oscilatory in the region beyond the classical turning point. In the quantum tunneling region inside the classical turning point, F is exponentially supressed.

Many numerical libraries compute Coulomb wave functions in the quantum tunneling region using a WKB approximation, which accurately determine only the first handfull of digits; our library computes Coulomb wave functions even in this computationaly difficult region to nearly full precision -- all but the last 3-4 digits can be trusted.

The irregular Coulomb wave functions GL(η,ρ) are the complementary independent solutions of the same differential equation.

Exceptions

ExceptionCondition
System..::..ArgumentOutOfRangeExceptionL or rho is negative.

See Also