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

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)

Function Documentation

◆ enk()

double DiracHydrogen::enk	(	PrincipalQN	n,
		DiracQN	k,
		Zeff	z,
		AlphaFS	a
	)

Energy, without rest mass.

◆ Enk()

double DiracHydrogen::Enk	(	PrincipalQN	n,
		DiracQN	k,
		Zeff	z,
		AlphaFS	a
	)

Enk = enk + c^2.

◆ gamma()

double DiracHydrogen::gamma	(	DiracQN	k,
		Zeff	z,
		AlphaFS	a
	)

Relativistic factor gamma = Sqrt[k^2 - (aZ)^2].

◆ f()

double DiracHydrogen::f	(	RaB	r,
		PrincipalQN	n,
		DiracQN	k,
		Zeff	z,
		AlphaFS	a
	)

Upper radial component.

◆ g()

double DiracHydrogen::g	(	RaB	r,
		PrincipalQN	n,
		DiracQN	k,
		Zeff	z,
		AlphaFS	a
	)

Lower (small) radial component.