ampsci
c++ program for high-precision atomic structure calculations of single-valence systems
Typedefs | Enumerations | Functions
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