SL(2,C)-invariant representation of the Dirac equation. II. Coulomb Green's function
The Kepler problem for the Klein--Gordon type wave equation )Pi/sub ..mu../Pi/sub ..mu../+m/sup 2/+iesigmax(E+iB))phi = 0, investigated earlier (J. Math. Phys. 23, 1179 (1982)) and proven to be equivalent to the conventional Dirac equation, is discussed. In this equation phi is a 2 x 1 Pauli spinor and sigma/sub a/, a = 1, 2, 3, are the usual 2 x 2 Pauli spin matrices. Quite simple expressions for the bound state Coulomb wavefunctions and for the Coulomb Green's function are obtained by exploiting the concept of ''coupling constant eigenfunction.'' To facilitate the direct use of these simple expressions in Coulomb calculations, a stationary state perturbation theory appropriate for the Klein--Gordon type wave equation itself is described.
- Research Organization:
- Physics Department, Wilkes College, Wilkes-Barre, Pennsylvania 18766
- OSTI ID:
- 5720286
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 24:9; ISSN JMAPA
- Country of Publication:
- United States
- Language:
- English
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
ANGULAR MOMENTUM OPERATORS
BOUND STATE
COULOMB FIELD
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EIGENFUNCTIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
GREEN FUNCTION
INVARIANCE PRINCIPLES
KLEIN-GORDON EQUATION
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PAULI SPIN OPERATORS
PERTURBATION THEORY
QUANTUM OPERATORS
WAVE EQUATIONS
WAVE FUNCTIONS