COULOMB GREEN'S FUNCTIONS AND THE FURRY APPROXIMATION
The Coulomb Green's function for the nonrelativistic Schrodinger equation is obtained in closed form, starting from the partial-wave expansion and using an integral represertation for a product of two Whittaker functions with different arguments. The Neumann's series for J/sub nu /(kz) is required in evaluating the sum on states. The Coulomb Green's functions for the Klein-Gordon and iterated Dirac equations are obtained in closed form in the Furry apc. The KleinGordon Green's function in this approximntion is shown to be at the same time the exact Green's function for the Klein-Gordon equation without the potential squared term. An alternate and very simple derivntion of the approximate Green's function for the iterated Dirac equation is given using perturbation theory. From tbis Green's function, an approximate Coulomb Green's function in closed form for the Dirac equation itself is constructed. Certain known results for Coulomb wavefunctions with modified plane -wave behavior at large distances are rederived using the foregoing methods and results. (auth)
- Research Organization:
- Stanford Univ., Calif.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-18-021027
- OSTI ID:
- 4006492
- Journal Information:
- Journal of Mathematical Physics (New York) (U.S.), Journal Name: Journal of Mathematical Physics (New York) (U.S.) Vol. Vol: 5; ISSN JMAPA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
Relativistic Coulomb Green's function in d dimensions
REPRESENTATIONS FOR THE NONRELATIVISTIC COULOMB GREEN'S FUNCTION