DiracHydrogen Namespace Reference

Exact relativistic hydrogen-like (Coulomb) wavefuntions. More...

Typedefs
using	DiracQN = qip::StrongType< DiracTypes::DiracQN, int >
using	AlphaFS = qip::StrongType< DiracTypes::AlphaFS, double >
using	Zeff = qip::StrongType< DiracTypes::Zeff, double >
using	PrincipalQN = qip::StrongType< DiracTypes::PrincipalQN, double >
using	RaB = qip::StrongType< DiracTypes::RaB, double >

Enumerations
enum class	DiracTypes {   DiracQN , AlphaFS , Zeff , PrincipalQN ,   RaB }

Functions
double	enk (PrincipalQN n, DiracQN k, Zeff z, AlphaFS a)
	Energy, without rest mass.
double	Enk (PrincipalQN n, DiracQN k, Zeff z, AlphaFS a)
	Enk = enk + c^2.
double	gamma (DiracQN k, Zeff z, AlphaFS a)
	Relativistic factor gamma = Sqrt[k^2 - (aZ)^2].
double	f (RaB r, PrincipalQN n, DiracQN k, Zeff z, AlphaFS a)
	Upper radial component.
double	g (RaB r, PrincipalQN n, DiracQN k, Zeff z, AlphaFS a)
	Lower (small) radial component.
double	gfratio (double r, int k, double z, double a, double e, double m)

Detailed Description

Exact relativistic hydrogen-like (Coulomb) wavefuntions.

in form phi = (1/r)(f O, ig O')

From: H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One-and Two-Electron Atoms (Plenum, New York, 1977).

Note: Uses some numerically unstable functions, including Gamma functions and confluent hypergeometric functions. So, for some inputs, may be numerically unstable. For reasonable inputs (i.e., Zeff=5, up to n=~10), good to at least parts in 10^12