Function qsym2::angmom::spinor_rotation_3d::dmat_euler_gen_element

pub fn dmat_euler_gen_element(
    twoj: u32,
    mdashi: usize,
    mi: usize,
    euler_angles: (f64, f64, f64),
) -> Complex<f64>

Returns an element in the Wigner rotation matrix for an integral or half-integral $j$, defined by

$$\hat{R}(\alpha, \beta, \gamma) \ket{jm}
= \sum_{m'} \ket{jm'} D^{(j)}_{m'm}(\alpha, \beta, \gamma).$$

The explicit expression for the elements of $\mathbf{D}^{(1/2)}(\alpha, \beta, \gamma)$ is given in Professor Anthony Stone’s graduate lecture notes on Angular Momentum at the University of Cambridge in 2006.

Arguments

• twoj - Two times the angular momentum $2j$. If this is even, $j$ is integral; otherwise, $j$ is half-integral.
• mdashi - Index for $m'$ given by $m'+\tfrac{1}{2}$.
• mi - Index for $m$ given by $m+\tfrac{1}{2}$.
• euler_angles - A triplet of Euler angles $(\alpha, \beta, \gamma)$ in radians, following the Whitaker convention, i.e. $z_2-y-z_1$ (extrinsic rotations).

Returns

The element $D^{(j)}_{m'm}(\alpha, \beta, \gamma)$.