An asymptotic expansion for the Green's function of nonrelativistic potential-scattering theory and the asymptotic character of the born series for the jost function for large complex angular momenta

1966 ◽  
Vol 42 (1) ◽  
pp. 39-66 ◽  
Author(s):  
O. Brander
Keyword(s):  
Asymptotic Expansion ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Theory ◽  
Potential Scattering ◽  
Angular Momenta ◽  
Born Series ◽  
Jost Function ◽  
Large Complex ◽  
Asymptotic Character

Parabolic Representations of Scattering Green’s Functions

1999 ◽  
Author(s):  
Paul E. Barbone
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Green’S Function ◽  
Inhomogeneous Medium ◽  
Green's Function ◽  
Free Space ◽  
Green's Functions ◽  
Green’S Functions

Abstract We derive a one-way wave equation representation of the “free space” Green’s function for an inhomogeneous medium. Our representation results from an asymptotic expansion in inverse powers of the wavenumber. Our representation takes account of losses due to scattering in all directions, even though only one-way operators are used.

On the asymptotic expansion of the static Green's function in cubic crystals

1970 ◽  
Vol 236 (1) ◽  
pp. 14-20 ◽  
Author(s):  
N. Angelescu ◽  
D. Grecu ◽  
G. Nenciu
Keyword(s):  
Asymptotic Expansion ◽  
Green’S Function ◽  
Green's Function ◽  
Cubic Crystals

scholarly journals Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

2014 ◽  
Vol 90 (20) ◽  
Author(s):  
Aftab Alam ◽  
Suffian N. Khan ◽  
A. V. Smirnov ◽  
D. M. Nicholson ◽  
Duane D. Johnson
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Scattering Theory ◽  
Basis Set ◽  
Multiple Scattering Theory

Precise theory of the Stark effect on hydrogen- and helium-like atoms

2002 ◽  
Vol 80 (11) ◽  
pp. 1401-1412 ◽  
Author(s):  
V D Ovsiannikov ◽  
V G Pal'chikov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ground State ◽  
Stark Effect ◽  
Energy Levels ◽  
Relativistic Effects ◽  
Model Potential ◽  
Matrix Elements ◽  
Angular Momenta ◽  
Relativistic Coulomb

The relativistic effects on the dipole polarizabilities and hyperpolarizabilities are considered for different kinds of energy levels in hydrogen- and helium-like atoms. The relativistic Coulomb Green's function is used for calculating the susceptibilities of the ground-state hydrogen up to terms of order (α Z)10. Both relativistic and interelectronic corrections are determined for the ground state of helium. The formulas are given for polarizability and hyperpolarizability in the relativistic "screened-charge" approximation. The anticrossing of the triplet 3PJ states with zero magnetic quantum number is studied on the basis of perturbation theory for degenerate states. General expressions are given for the dipole matrix elements, up to the fourth order in field strength, within the basis of close fine-structure substates with equal angular momenta L and different total momenta J. The calculation of the higher order matrix elements is carried out with the use of the Green's function in the model potential approximation. PACS Nos.: 31.10Dk, 31.15Ar, 31.30Jv, 32.10-f, 31.25Eb

On the Green’s function of potential scattering

1963 ◽  
Vol 28 (3) ◽  
pp. 547-566 ◽  
Author(s):  
M. Verde
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Potential Scattering
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