CoulombF Method (L, eta, rho)

Computes the regular Coulomb wave function.

Declaration Syntax

Visual Basic

Visual C++

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 F_L(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 G_L(η,ρ) are the complementary independent solutions of the same differential equation.

Exceptions

Exception	Condition
ArgumentOutOfRangeException	L or rho is negative.