Study: Screened Coulomb vs. Double-Split Architecture
link to the script -> here
running the script : python examples/screened_coulomb_study.py
gives this output
The plot that we get after the script runs is this :
hence what we can say from this is that the Screened Coulomb method is a lose-lose. It doesn't solve the numerical instability at the nuclear cusp ($r=0$), and it severely distorts the physical accuracy of the potential everywhere else. Our Double-Split method is valid , it analytically neutralizes the cusp while preserving the exact 1/r physics with an error of $10^{-6}$.
Study: Screened Coulomb vs. Double-Split Architecture
link to the script -> here
running the script :
python examples/screened_coulomb_study.pygives this output
The plot that we get after the script runs is this :
hence what we can say from this is that the Screened Coulomb method is a lose-lose. It doesn't solve the numerical instability at the nuclear cusp ($r=0$ ), and it severely distorts the physical accuracy of the potential everywhere else. Our Double-Split method is valid , it analytically neutralizes the cusp while preserving the exact 1/r physics with an error of $10^{-6}$ .