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