treams.lattice.dsumcw1d

treams.lattice.dsumcw1d(l, k, kpar, a, r, i) = <ufunc 'dsumcw1d'>

Direct summation of cylindrical functions on a 1d lattice

Computes

\[D_{l}(k, k_\parallel, r, \Lambda_1) = \sum_{R \in \Lambda_1} H_l^{(1)}(k |r + R|) (\mathrm{sign}(-r - R))^l \mathrm e^{\mathrm i k_\parallel R}\]

directly for one expansion value i. Sum i from 0 to a large value to obtain an approximation of the sum value. In a the lattice vectors are given as rows. The lattice is along the x axis.

Parameters:

  • l (integer) – Order

  • k (float or complex) – Wave number

  • kpar (float) – Tangential wave vector component

  • a (float) – Lattice pitch

  • r (float) – In-line shift

  • i (integer) – Expansion value

Returns:

complex