public static SolutionPair Coulomb( int L, double eta, double rho )
Public Shared Function Coulomb ( L As Integer, eta As Double, rho As Double ) As SolutionPair
public: static SolutionPair Coulomb( int L, double eta, double rho )
static member Coulomb : L : int * eta : float * rho : float -> SolutionPair
|ArgumentOutOfRangeException||L or rho is negative.|
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 and vanishes at the origin, while G grows exponentially and diverges at the origin.
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.