treams.lattice.lsumsw1d

treams.lattice.lsumsw1d(l, k, kpar, a, r, eta) = <ufunc 'lsumsw1d'>

Fast summation of spherical functions on a 1d lattice

Computes

\[D_{l0}(k, k_\parallel, \Lambda_1, r) = \sum_{R \in \Lambda_1} h_l^{(1)}(k |r + R|) Y_{l0}(-\boldsymbol{\hat z} (r + R)) \mathrm e^{\mathrm i k_\parallel R}\]

using the Ewald summation.

The cut between the real and reciprocal space summation is defined by eta. Larger values increase the weight of the real sum. The lattice is along the z-axis. Therefore only \(m = 0\) contributes.

Parameters:

• l (integer) – Degree \(l \geq 0\)

• k (float or complex) – Wave number

• kpar (float) – Tangential wave vector component

• a (float) – Lattice pitch

• r (float) – In-line shift

• eta (float or complex) – Separation value

Returns:

complex