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Coulomb functions: variables ?,?

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1: 33.24 Tables
§33.24 Tables
2: 33.25 Approximations
§33.25 Approximations
3: 33.20 Expansions for Small | ϵ |
§33.20(i) Case ϵ = 0
§33.20(ii) Power-Series in ϵ for the Regular Solution
§33.20(iii) Asymptotic Expansion for the Irregular Solution
where A ( ϵ , ) is given by (33.14.11), (33.14.12), and …
§33.20(iv) Uniform Asymptotic Expansions
4: 33.2 Definitions and Basic Properties
§33.2(i) Coulomb Wave Equation
The function F ( η , ρ ) is recessive (§2.7(iii)) at ρ = 0 , and is defined by … The functions H ± ( η , ρ ) are defined by … …
§33.2(iv) Wronskians and Cross-Product
5: 33.17 Recurrence Relations and Derivatives
§33.17 Recurrence Relations and Derivatives
33.17.1 ( + 1 ) r f ( ϵ , 1 ; r ) ( 2 + 1 ) ( ( + 1 ) r ) f ( ϵ , ; r ) + ( 1 + ( + 1 ) 2 ϵ ) r f ( ϵ , + 1 ; r ) = 0 ,
33.17.2 ( + 1 ) ( 1 + 2 ϵ ) r h ( ϵ , 1 ; r ) ( 2 + 1 ) ( ( + 1 ) r ) h ( ϵ , ; r ) + r h ( ϵ , + 1 ; r ) = 0 ,
33.17.3 ( + 1 ) r f ( ϵ , ; r ) = ( ( + 1 ) 2 r ) f ( ϵ , ; r ) ( 1 + ( + 1 ) 2 ϵ ) r f ( ϵ , + 1 ; r ) ,
33.17.4 ( + 1 ) r h ( ϵ , ; r ) = ( ( + 1 ) 2 r ) h ( ϵ , ; r ) r h ( ϵ , + 1 ; r ) .
6: 33.18 Limiting Forms for Large
§33.18 Limiting Forms for Large
7: 33.14 Definitions and Basic Properties
§33.14(i) Coulomb Wave Equation
§33.14(ii) Regular Solution f ( ϵ , ; r )
§33.14(iii) Irregular Solution h ( ϵ , ; r )
§33.14(iv) Solutions s ( ϵ , ; r ) and c ( ϵ , ; r )
§33.14(v) Wronskians
8: 33.22 Particle Scattering and Atomic and Molecular Spectra
𝗄 Scaling
Z Scaling
i 𝗄 Scaling
§33.22(iii) Conversions Between Variables
9: 33.23 Methods of Computation
§33.23 Methods of Computation
§33.23(vii) WKBJ Approximations
10: 33.1 Special Notation
  • Greene et al. (1979):

    f ( 0 ) ( ϵ , ; r ) = f ( ϵ , ; r ) , f ( ϵ , ; r ) = s ( ϵ , ; r ) , g ( ϵ , ; r ) = c ( ϵ , ; r ) .