Numerical conversion of full spectra into forces

The integration over is considerably shortened if we convert to = 10v and make v a variable that goes from a finite value to infinity. The integration in v is itself effected as a summation of steps Av = 0.1 (or whatever increment makes sense for the problem)  

PROBLEM L2.19 When can the discrete-sampling frequency summation be replaced with an integral over an imaginary frequency Show that the condition 

Numerical conversion of full spectra into forces 

To show features at higher frequencies, the function Re[/cv0 R) multiplies s ( r) by whereas e(i ) depends on e ( vR) weighted by the first power of g r. These s(/ ) are then used to compute Hamaker coefficients (in 1 zj = 10-21 J) in the limit of no retardation for attraction across a vacuum13 or across water14 as in this table  

Even exhaustive full-spectral computations have their frustrating uncertainties. Compare these tabulated Hamaker coefficients with those in parentheses,15 quoted in the Prelude, which used earlier, slightly different, data and slightly different procedures16 to create e(/ ). The comparison reminds us to continue to search for the best data and to be aware of the unavoidable ambiguities due to limited data and to computational procedure. 

---

L2.4.A. Properties of dielectric response, 241 L2.4.B. Integration algorithms, 261 L2.4.C. Numerical conversion of full spectra into forces, 263 L2.4.D. Sample spectral parameters, 266 L2.4.E. Department of tricks, shortcuts, and desperate necessities, 270 L2.4.F. Sample programs, approximate procedures, 271... 

L.2.4.C. NUMERICAL CONVERSION OF FULL SPECTRA INTO FORCES... 

L.2.4.C. Numerical conversion of full spectra into forces... 

---

See also in sourсe #XX -- [ ]

---