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Next: 6.1 Multipole Expansion Up: On Convergence Acceleration of Previous: 5 A Simple Example

6 Numerical Tests

  We study the charge density tex2html_wrap_inline2800 of Eq. (42) in the last section for tex2html_wrap_inline2802 , tex2html_wrap_inline2804 and tex2html_wrap_inline2806 , where tex2html_wrap_inline2808 is the unit vector in z direction. It is rotationally symmetric around the z axis. This density is also plotted in http://www.chemie.uni-regensburg.de/ECCC/4/rho.ps as a function of x and z for y=0.

The corresponding electrostatic potential is also rotationally symmetric around the z axis, a function of z and tex2html_wrap_inline2824 only or, equivalently, only of tex2html_wrap_inline2826 and tex2html_wrap_inline2520 with tex2html_wrap_inline2830 . This is also valid for the multipole expansion (47) and the exact expansion (45) in spherical harmonics.




next up previous external
Next: 6.1 Multipole Expansion Up: On Convergence Acceleration of Previous: 5 A Simple Example

Herbert H. H. Homeier (herbert.homeier@na-net.ornl.gov)