treams.SphericalWaveBasis.default

classmethod SphericalWaveBasis.default(lmax, nmax=1, positions=None)

Default basis for the given maximal multipolar order.

The default order contains separate blocks for each position index which are in ascending order. Within each block the modes are sorted by angular momentum \(l\), with the lowest angular momentum coming first. For each angular momentum its z-projection is in ascending order from \(m = -l\) to \(m = l\). Finally, the polarization index is the fastest changing index which iterates between 1 and 0.

Example

>>> SphericalWaveBasis.default(2)
SphericalWaveBasis(
    pidx=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0],
    l=[1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2],
    m=[-1 -1  0  0  1  1 -2 -2 -1 -1  0  0  1  1  2  2],
    pol=[1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0],
    positions=[[0. 0. 0.]],
)
>>> SphericalWaveBasis.default(1, 2, [[0, 0, 1.], [0, 0, -1.]])
SphericalWaveBasis(
    pidx=[0 0 0 0 0 0 1 1 1 1 1 1],
    l=[1 1 1 1 1 1 1 1 1 1 1 1],
    m=[-1 -1  0  0  1  1 -1 -1  0  0  1  1],
    pol=[1 0 1 0 1 0 1 0 1 0 1 0],
    positions=[[ 0.  0.  1.], [ 0.  0. -1.]],
)

Parameters:

• lmax (int) – Maximal multipolar order.

• nmax (int, optional) – Number of positions, defaults to 1.

• positions (array-like, optional) – Positions of the origins.