Premium
The radial wavefunction of a relativistic binary of two fermions bound by the Coulomb force
Author(s) -
Marsch E.
Publication year - 2007
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200610248
Subject(s) - brst quantization , physics , gauge symmetry , lagrange multiplier , symmetry (geometry) , gauge theory , gauge (firearms) , coulomb , wave function , gauge anomaly , gauge fixing , theoretical physics , quantum gauge theory , mathematical physics , hamiltonian lattice gauge theory , quantum mechanics , gauge boson , mathematics , geometry , archaeology , history , electron
The exact radial eigenfunctions of a relativistic binary atom bound by the static Coulomb force are calculated. We consider the two‐fermion Dirac equation for two distinguishable fermions (like, e.g., in positronium) including the static Coulomb potential but no radiative corrections. As shown in a previous paper and its addendum this problem can be solved exactly [1]. Here we provide the exact solution in terms of generalized hypergeometric functions for the radial eigenfunctions of the hamiltonian, which are determined through a matrix recursion relation. Also, an equivalent set of coupled first‐order, or uncoupled second‐order, differential equations that may be solved numerically is provided.