.kwf — Momentum-Space Probability Density

Generated when the -k --kwf flag is provided for the first$n $excitons chosen with -n --states [n=8].

The .kwf file stores the momentum-space probability density of each exciton wavefunction. It quantifies how the exciton is distributed over electron-hole pairs with a well-defined crystal momentum $\mathbf{k}$.

Format

The file contains a table with one row per k-point and one column per exciton state:

kx ky kz P
.
.
.
#
kx ky kz P
.
.
.
#

Units

$[k]= Å ^{-1}$
$\left| \psi_{X}(\bm{k})^{2} \right|$ is dimensionless and normalized over the k-grid

Definition

Given the exciton wavefunction expressed in the electron-hole basis as $A^{Q}_{vc}(\mathbf{k})$, the $k$ space probability is defined as:

\[|\psi_{X}(\bm{k})|^2 = \sum_{v,c} \left| A^{Q}_{vc}(\bm{k}) \right|^2\]

This quantity is evaluated on the same k-point grid used in the original BSE calculation.