Function qsym2::angmom::spinor_rotation_3d::dmat_angleaxis

pub fn dmat_angleaxis(
    angle: f64,
    axis: Vector3<f64>,
    increasingm: bool,
) -> Array2<Complex<f64>>

Returns the Wigner rotation matrix for $j = 1/2$ whose elements are defined by

\hat{R}(\phi\hat{\mathbf{n}}) \ket{\tfrac{1}{2}m}
= \sum_{m'} \ket{\tfrac{1}{2}m'} D^{(1/2)}_{m'm}(\phi\hat{\mathbf{n}}).

The parametrisation of $\mathbf{D}^{(1/2)}$ by $\phi$ and $\hat{\mathbf{n}}$ is given in (4-9.12) of Altmann, S. L. Rotations, Quaternions, and Double Groups. (Dover Publications, Inc., 2005).

Arguments

• angle - The angle $\phi$ of the rotation in radians. A positive rotation is an anticlockwise rotation when looking down axis.
• axis - A space-fixed vector defining the axis of rotation. The supplied vector will be normalised.
• increasingm - If true, the rows and columns of $\mathbf{D}^{(1/2)}$ are arranged in increasing order of $m_l = -l, \ldots, l$. If false, the order is reversed: $m_l = l, \ldots, -l$. The recommended default is false, in accordance with convention.

Returns

The matrix $\mathbf{D}^{(1/2)}(\phi\hat{\mathbf{n}})$.