ampsci
c++ program for highprecision atomic structure calculations of singlevalence systems

Exact relativistic hydrogenlike (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.  
Exact relativistic hydrogenlike (Coulomb) wavefuntions.
in form phi = (1/r)(f O, ig O')
From: H. A. Bethe and E. E. Salpeter, Quantum Mechanics of Oneand TwoElectron 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