acoustotreams.special.ssw_psi

acoustotreams.special.ssw_psi(l, m, x, y, z, theta, phi, k)

Far-field amplitude of singular scalar spherical wave \(\psi\)

Defined by

\[\psi_{lm}(x, y, z, \theta, \varphi) = \frac{\mathrm{i}^{-l-1}}{k} Y_{lm}(\theta, \varphi) \mathrm{e}^{-\mathrm{i} k \left(x \sin \theta \cos \varphi + y \sin \theta \sin \varphi + z \cos \theta\right)}\]

with acoustotreams.special.sph_harm().

This function describes a solution to the vector Helmholtz wave equation in the limit of \(kr \to +\infty\).

Parameters:

• l (int, array_like) – Degree \(l \geq 0\)

• m (int, array_like) – Order \(|m| \leq l\)

• x (float or complex, array_like) – X coordinate of the source

• y (float or complex, array_like) – Y coordinate of the source

• z (float or complex, array_like) – Z coordinate of the source

• theta (float or complex, array_like) – Polar angle

• phi (float, array_like) – Azimuthal angle

• k (float or complex, array_like) – Wave number in the medium

Returns:

complex