ABSTRACT
The electron density ̺(~r) can be considered the “diagonal element” of a more complex entity, the “spinless first-order density matrix” ̺1(~r;~r
′).∗ The name “density matrix” is somewhat conventional, as it has continuous “rows” and
“columns” ~r and ~r ′, respectively. The “diagonal element” means that we substitute~r ′ =~r into ̺1(~r;~r ′):
If in terms of a (finite or infinite) basis of one-electron functions {χµ} the electron density has an expansion (3.16), then the spinless first-order density
matrix can be expressed with the aid of the same matrix elements Dµν as
̺1(~r;~r ′) = ∑
′)χµ(~r) . (4.2)
where D is a matrix in the usual sense, i.e., its elements Dµν depend on two
discrete variables (the row and column indices). The equality (4.1) connects
this expression with the expansion (3.16) of the electron density.
