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.

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