mindchemistry.e3.o3.wigner_D

mindchemistry.e3.o3.wigner_D(l, alpha, beta, gamma)[source]

Wigner D matrix representation of SO(3).

It satisfies the following properties: * \(D(\text{identity rotation}) = \text{identity matrix}\) * \(D(R_1 \circ R_2) = D(R_1) \circ D(R_2)\) * \(D(R^{-1}) = D(R)^{-1} = D(R)^T\)

Parameters

l (int) – degree of representation.
alpha (Union[Tensor[float32], List[float], Tuple[float], ndarray[np.float32], float]) – rotation \(\alpha\) around Y axis, applied third.
beta (Union[Tensor[float32], List[float], Tuple[float], ndarray[np.float32], float]) – rotation \(\beta\) around X axis, applied second.
gamma (Union[Tensor[float32], List[float], Tuple[float], ndarray[np.float32], float]) – rotation \(\gamma\) around Y axis, applied first.

Returns

Tensor, Wigner D matrix \(D^l(\alpha, \beta, \gamma)\). The shape of Tensor is \((2l+1, 2l+1)\).

Supported Platforms:: Ascend

Examples

>>> from mindchemistry.e3.o3 import wigner_D
>>> m = wigner_D(1,1,1,1)
>>> print(m)
[[-0.09064701  0.7080733   0.70029646]
[ 0.7080733   0.54030234 -0.45464867]
[-0.7002964   0.45464864 -0.5503447 ]]