integrate.odeintto integrate the one-electron Schroedinger equation\n", "\n", "\\begin{equation}\n", " -u^{''}(r) + \\left(\\frac{l(l+1)}{r^2}-\\frac{2 Z}{r}\\right)u(r)\n", " = \\varepsilon u(r).\n", "\\end{equation}\n", "Here $\\psi_{lm}(\\vec{r}) = \\frac{u(r)}{r} Y_{lm}(\\hat{r})$, distance is measured in units of bohr radius and energy units is Rydberg ($1 Ry = 13.6058...eV$)\n", "
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optimize.brentq,to compute zero to very high precision. Store the index and the energy of the bound state for further processing.
\n", " Populate first $Z$ lowest laying electron states and\n", " compute \n", " $\\rho = \\sum_{lm\\in occupied} u_{lm}^2(r)/(4\\pi r^2)$. \n", " Each state with quantum number $l$ can take $2(2l+1)$\n", " electrons. Be carefull, if atom is not one of the Nobel gases\n", " (He, Ne, ...) the last orbital is only partially filled.\n", "\n", "