Determination of the quantum density matrix from experiment: An application to positron annihilation

This paper presents a simple method for determining a one-particle quantum density matrix for an electronic system using experimental data as input. The resulting matrix has proper trace value and is idempotent as required by quantum mechanics. With the use of this method the density matrix is calculated for two different model systems and for a Cu-Ge alloy. The population of the s, p, and d states of part of a band of the alloy are determined from the resulting matrix. The effect of symmetry on the technique is clarified and the inclusion of a positron wave function for momentum-density measurements is outlined.