arc.alkali_atom_functions.NumerovBack#

NumerovBack(innerLimit: float, outerLimit: float, kfun: Callable, step: float, init1: float, init2: float)[source]#

Full Python implementation of Numerov integration

Calculates solution function \(rad(r)\) with descrete step in \(r\) size of step, integrating from outerLimit towards the innerLimit (from outside, inwards) equation \(\frac{\mathrm{d}^2 rad(r)}{\mathrm{d} r^2} = kfun(r)\cdot rad(r)\).

Parameters:

  • innerLimit (float) – inner limit of integration

  • outerLimit (flaot) – outer limit of integration

  • kfun (function(double)) – pointer to function used in equation (see longer explanation above)

  • step – descrete step size for integration

  • init1 (float) – initial value, rad`(`outerLimit`+`step)

  • init2 (float) – initial value, rad`(`outerLimit`+:math:`2cdot step)

Returns:

\(r\) (a.u), \(rad(r)\);

Return type:

numpy array of float , numpy array of float, int

Note

Returned function is not normalized!

Note

If AlkaliAtom.cpp_numerov swich is set to True (default), much faster C implementation of the algorithm will be used instead. That is recommended option. See documentation installation instructions for more details.