treams.lattice.dsumcw1d_shift

treams.lattice.dsumcw1d_shift(l, k, kpar, a, r, i) = <ufunc 'dsumcw1d_shift'>

Direct summation of cylindrical functions on a 1d lattice with out of lattice shifts

Computes

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

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, (2,)-array) – Shift vector

• i (integer) – Expansion value

Returns:

complex