treams.lattice.dsumcw2d

treams.lattice.dsumcw2d(l, k, kpar, a, r, i) = <ufunc 'dsumcw2d'>

Direct summation of cylindrical functions on a 2d lattice

Computes

\[D_{l}(k, \boldsymbol k_\parallel, \boldsymbol r, \Lambda_2) = \sum_{\boldsymbol R \in \Lambda_2} H_l^{(1)}(k |\boldsymbol r + \boldsymbol R|) \mathrm e^{\mathrm i l \varphi_{-\boldsymbol r - \boldsymbol R}} \mathrm e^{\mathrm i \boldsymbol k_\parallel \boldsymbol R}\]

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.

Parameters:

• l (integer) – Order

• k (float or complex) – Wave number

• kpar (float, (2,)-array) – Wave vector

• a (float, (2,2)-array) – Lattice vectors

• r (float, (2,)-array) – Shift vector

• i (integer) – Expansion value

Returns:

complex