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.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 :math:`\mathbf{k}`.

Format
=======

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

.. code-block:: text

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

**Units**

* :math:`[k]= Å ^{-1}`

* :math:`\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 :math:`A^{Q}_{vc}(\mathbf{k})`, the $k$ space probability is defined as:

.. math::

   |\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.