qspec.doppler_3d  (  k ,  v ,  return_frame = 'atom' ,  axis = -1  )[source]

The 3D Doppler shift of the 3-vector $\vec{k}$ $$ k^{\prime\mu} = \Lambda^\nu_\mu(\pm\vec{v})k^\mu, $$ with the Lorentz-boost matrix $\Lambda_\nu^\mu$.

Parameters:

karray_like

The 3-vector $\vec{k}$ of light. Must have size 3 in the specified axis (arb. units).

varray_like

The velocity 3-vector $\vec{v}$. Must have size 3 in the specified axis (m/s).

return_frameNone

The coordinate system in which the frequency is returned. Can be either 'atom' or 'lab'.

axisNone

The axis along which the vector components are aligned.

Returns:

k_boostedndarray

the Doppler-shifted 3-vector $\vec{k}^{\prime}$ in either the rest frame of the atom or the laboratory frame ([k]).

Raises:

ValueError

rest_frame must be either 'atom' or 'lab'. The shapes of k and v must be compatible.