Density matrix in Momentum Space

[Morberticus]

I have an one-body density matrix in a Sine wave basis set (Thus psi = psi*). Unfortunately, these are not the natural orbitals (I have correlated particles), so I have off-diagonal elements. I believe I know how to extract the charge density from this density matrix

[itex]\rho(x;x') = \sum_{ij} c_{ij}\psi_i(x)\psi_j(x')[/itex]

Where x' = x. Can I do something similar to extract a "momentum density"?

[itex]\rho(k;k') = \sum_{ij} c_{ij}\psi_i(k)\psi_j(k')[/itex]


Where k' = k?

Thanks

 

[BigJDubs]

for your help. Yes, you can do something similar to extract a "momentum density" from the one-body density matrix. The formula you provided is correct. You just have to substitute k for x in the formula and use the momentum space wave functions instead of the position space wave functions.