sarkas.utilities.maths.yukawa_green_function

sarkas.utilities.maths.yukawa_green_function(k, alpha, kappa)

Evaluate the Green’s function of Coulomb/Yukawa potential.

\[G(k) = \frac{4 \pi }{\kappa^2 + k^2} e^{- (k^2 + \kappa^2)/4 \alpha^2 }\]

Parameters

• k (float, numpy.ndarray) – Range or value at which to calculate the function.

• alpha (float) – Ewald screening parameter.

• kappa (float) – Inverse screening length.

Return type

float

Returns

_ (numpy.ndarray, float) – Green’s function. See equation above

Examples

>>> import numpy as np
>>> k = np.linspace(0, 2, 100)
>>> alpha = 0.2
>>> kappa = 0.5
>>> G_k = yukawa_green_function(k = k, alpha = alpha, kappa = kappa)