Closed form of the generalized Green’s function for the Helmholtz operator on the two-dimensional unit sphere

2006 ◽  
Vol 47 (6) ◽  
pp. 063506 ◽  
Author(s):  
Radosław Szmytkowski
Keyword(s):  
Green’S Function ◽  
Closed Form ◽  
Green's Function ◽  
Unit Sphere ◽  
Two Dimensional ◽  
Helmholtz Operator ◽  
Dimensional Unit

scholarly journals Green’s function for the semi-infinite strip in terms of an improper integral

2020 ◽  
Vol 17 (2) ◽  
pp. 235-246
Author(s):  
Dragan Filipovic ◽  
Tatijana Dlabac
Keyword(s):  
Green’S Function ◽  
Closed Form ◽  
Green's Function ◽  
Infinite Strip ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Improper Integral

In this paper Green?s function for the semi-infinite strip (which is the two-dimensional Green?s function for a groove of infinite depth and length) is determined in the form of an improper integral, as opposed to the standard summation form. The integral itself, although rather complex, is found in a closed form. By using the derived Green?s function simple formulas are obtained for a single and two-wire line configurations inside the groove.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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